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General Physics 2
Quarter 4 - Module 6
Atomic and Nuclear Phenomena
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General Physics 2 – Grade 12
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Quarter 4 - Module 6: Atomic and Nuclear Phenomena
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Senior
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General Physics
Quarter 4 - Module 6
Atomic and Nuclear Phenomena
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Table of Contents
What This Module is About ............................................................................................................ i
What I Need to Know ...................................................................................................................... ii
How to Learn from this Module .................................................................................................... .ii
Icons of this Module ....................................................................................................................... iii
What I Know ................................................................................................................................... .iii
Fourth Quarter – Module 6
Lesson 1: Photoelectric Effect
What’s In ................................................................................................... 1
What I Need To Know ............................................................................. 1
What’s New ............................................................................................... 2
What Is It ................................................................................................... 2
What’s More .............................................................................................. 5
What I Can Do........................................................................................... 6
Lesson 2: Atomic Spectra
What’s In ................................................................................................... 7
What I Need To Know ............................................................................. 7
What’s New ............................................................................................... 7
What Is It ................................................................................................... 8
What’s More .............................................................................................. 11
What I Can Do........................................................................................... 11
Lesson 3: Radioactive Decay
What’s In ................................................................................................... 12
What I Need To Know ............................................................................. 12
What’s New ............................................................................................... 12
What Is It ................................................................................................... 13
What’s More .............................................................................................. 16
What I Can Do........................................................................................... 16
Summary .......................................................................................................................
17
Assessment: (Post-Test) ................................................................................................
18
Key to Answers ..............................................................................................................
20
References ....................................................................................................................
i
21
Module 6
Atomic and Nuclear Phenomena
What This Module is About
This module demonstrates your understanding on the concepts of Atomic and
Nuclear Phenomena and how Scientists were able to explain it using the particle-like
behavior of light.
All matter is made up of atoms. Our knowledge of atoms made us understand
the basic properties of the states of matter – solid, liquid and gas. And going deeper
in studying its subatomic particles, using the concept of nuclear atom which is
composed of the electrons around the nucleus and the particles inside the nucleus,
the protons and neutrons, opens the fundamental basis of the modern view of the
world.
Specifically, this module will discuss three (3) lessons:
•
•
•
Lesson 1 – Photoelectric Effect
Lesson 2 – Atomic Spectra
Lesson 3 – Radioactive Decay
What I Need to Know
At the end of this module, you should be able to:
1. Explain the photoelectric effect using the idea of light quanta or photons
STEM_GP12MPIVh-45
2. Explain qualitatively the properties of atomic emission and absorption spectra using
the concept of energy levels STEM_GP12MPIVh-46
3. Calculating radioisotope activity using the concept of half-life STEM_GP12MPIVh-i47
ii
How to Learn from this Module
To achieve the objectives cited above, you are to do the following:
•
Take your time reading the lessons carefully.
•
Follow the directions and/or instructions in the activities and exercises diligently.
•
Answer all the given tests and exercises.
Icons of this Module
What I Need to
This part contains learning objectives that
Know
are set for you to learn as you go along the
module.
What I know
This is an assessment as to your level of
What’s In
knowledge to the subject matter at hand,
meant specifically to gauge prior related
knowledge
This part connects previous lesson with that
of the current one.
What’s New
An introduction of the new lesson through
various activities, before it will be presented
to you
What is It
These are discussions of the activities as a
way to deepen your discovery and understanding of the concept.
What’s More
These are follow-up activities that are intended for you to practice further in order to
master the competencies.
What I Have
Learned
Activities designed to process what you
have learned from the lesson
What I can do
These are tasks that are designed to showcase your skills and knowledge gained, and
applied into real-life concerns and situations.
iii
What I Know
Multiple Choice. Answer the question that follows. Choose the best answer from the
given choices.
1. Photoelectric effect was explained by
a. Einstein
b. Faraday
c. Plank
d. Hertz
2. Photoelectrons stopping potential depends on
a. Frequency of incident light and nature of the cathode material
b. The intensity of the incident light
c. The frequency of the incident light
d. Nature of cathode material
3. The minimum energy required to remove an electron is called
a. Stopping potential
b. Kinetic energy
c. Work function
d. None of these
4. When talking about energy levels in an atom, what is an "excited state"?
a. The highest energy state of an atom.
b. The lowest energy state of an atom.
c. Any level higher than the ground state.
d. When an atom loses an electron
5. Why are line emission spectra of elements called "atomic fingerprints"?
a. They are all the same
c. They are all unique
b. They are all similar
d. They all contain colored light
6. Which type of spectrum is this?
a. Emission Spectrum
b. Absorption Spectrum
c. Continuous Spectrum
7. Radioactivity may be detected by which
one of the following instruments?
a. Atomic clock
c. Ratemeter
b. Geiger-Muller tube
d. Multimeter
8. Radioactive substances must be handled carefully because they emit
a. radiation which damage living cells
b. electrically charged particles
c. protons, neutrons and electrons
d. rays which makes substances radioactive
9. Isotopes of the same element have different
a. numbers of protons
c. atomic numbers
b. numbers of neutrons
d. numbers of electrons
10. All radioactive sources have a half-life. Which statement about the half-life of a source is
correct?
a. It is half the time for the radioactive source to become safe
b. It is half the time it takes for an atom to decay
c. It is half the time it takes the activity of the source to decrease to zero
d. It is the time it takes the activity of the source to decrease by half
iv
Lesson
1
The Photoelectric Effect
What’s In
In 1939, Alexandre Edmond Becquerel conducted a study on the effect of light
on electrolytic cells and discovered the photovoltaic effect. The photovoltaic effect is
a process that generates voltage or electric current in a photovoltaic cell when it is
exposed to sunlight. His work was instrumental in showing a strong relationship
between light and the electronic properties of materials.
Another phenomena leading to understanding deeper the nature of light was
discovered. The actual Photoelectric Effect was first observed by Heinrich Hertz in
1887, the phenomenon is also known as the Hertz effect. Several studies about this
phenomenon were conducted but was found hard to explain using the classical
definition on the nature of light – its wave-like behavior
What I Need To Know
This lesson will help us understand how Photoelectric Effect was explained
using the idea of light quanta or photons STEM_GP12MPIVh-45
1
What’s New
Unscramble the word/s inside the box to complete the concept map of Photoelectric
Effect. Write your answer in a separate paper
What Is It
THE PHOTOELECTRIC EFFECT
The photoelectric effect is a
phenomenon in which electrons
are ejected from the surface of a
metal when light is incident on it.
These ejected electrons are called
photoelectrons.
In order to escape from the
metal surface, these electrons
must absorb enough energy from the incident light to overcome its attraction to the positive
ions in the metal. This minimum energy needed by the electrons is called the Work Function
denoted by ∅.
2
The figure shows the set-up
of
the
Photoelectric
Effect
Experiment.
Enclosed in the vacuum tube
are two plates; the Emitter and the
Collector, acting as the cathode and
anode respectively. These two plates
are connected to a Power Supply
and an Ammeter which measures
the current caused by the movement
of ejected electrons.
The Photoelectric Effect was first observed by Heinrich Hertz in 1887 during his
experiment on Electromagnetic Waves. He noticed that a spark would jump readily between
two electrically charged spheres when their surfaces were illuminated by the light from another
spark.
In the year 1886 – 1900, two German Physicists Wilhelm Hallwachs and Philipp Lenard
investigated in detail the Photoelectric Effect.
However, the results of their experiments are hard to understand on the basis of
classical Physics.
In 1905, Albert Einstein developed the correct analysis of the Photoelectric Effect on
the basis of Max Planck’s experiment on blackbody radiation which suggested the particle-like
nature of light.
Einstein postulated that a beam of light consists of small packages of energy called
photons. And was able to formulate the energy of the photon in the equation:
𝐸 = ℎ𝑓 =
ℎ𝑐
λ
where
ℎ = 6.626𝑥10−34 𝐽. 𝑠 = 4.14𝑥10−14 𝑒𝑉. 𝑠 (Planck’s Constant)
𝑓 = 𝑐/λ is the frequency of the light
𝑐 = is the speed of light (in a vacuum)
λ = is the wavelength of the light
3
Einstein also applied the Conservation of Energy to calculate the maximum kinetic
energy of the photoelectrons and formulated the equation:
𝐾𝐸𝑚𝑎𝑥 = 𝐸 − ∅
In terms of the stopping potential, 𝑉𝑜, the above formula can be written as
𝑒𝑉𝑜 = 𝐸 − ∅
where
𝐾𝐸𝑚𝑎𝑥 = 𝑒𝑉𝑜
The stopping potential, 𝑉𝑜, is the voltage difference required to stop electrons from
moving between plates.
From the Conservation of Energy equation, the following predictions can be made:
In conclusion, the Photoelectric Effect Phenomenon contributed significantly in the
development of Modern Physics which finally resolved the controversy on the nature of light:
particle-like versus the wave-like behavior. The results remain important for research in areas
from material science to astrophysics as well as forming the basis for a variety of useful
devices.
Sample Problem:
Using the experimental apparatus shown in the figure, when
an ultraviolet light with a wavelength 0f 240nm shines on a
particular metal plate, electrons are emitted from plate 1,
crossing the gap to plate 2 and causing a current to flow
through the wire connecting the two plates. The battery
voltage is gradually increased until the current in the ammeter
drops to zero, at which point the battery voltage is 1.40V.
a.
b.
c.
d.
What is the energy of the photons in the beam of light, in eV?
What is the maximum kinetic energy of the emitted electrons, in eV?
What is the Work Function of the metal?
What is the longest wavelength that would cause electrons to be emitted, for this
particular metal?
e. Is this wavelength in the visible spectrum? If not, in what part of the spectrum is
this light found?
4
Solution:
3.00𝑥108 𝑚
𝑐
𝑠
−15
a. 𝐸 = ℎ𝑓 = ℎ λ = (4.136𝑥10−15 𝑒𝑉. 𝑠) 2.40𝑥10
𝑒𝑉. 𝑠)(1.25𝑥1015 /𝑠) = 5.17𝑒𝑉
−7 𝑚 = (4.136𝑥10
b. The maximum kinetic energy of the emitted electrons is related to the minimum voltage
across the two plates needed to stop the electrons from reaching the second plate (known
as the stopping potential). In this case, the stopping potential is 1.40eV, so the maximum
kinetic energy of the electrons is 1.40eV
c. 𝐾𝐸𝑚𝑎𝑥 = 𝐸 − ∅
→ ∅ = 𝐸 − 𝐾𝐸𝑚𝑎𝑥 = 5.17𝑒𝑉 − 1.40𝑒𝑉 = 3.77𝑒𝑉
d. The maximum wavelength that would cause electrons to be emitted corresponds to the
threshold frequency for this situation. Let’s first determine the threshold frequency, 𝑓𝑜 .
∅ = ℎ 𝑓𝑜 → 𝑓𝑜 =
∅
ℎ
=
3.77𝑒𝑉
4.136𝑥10−15 𝑒𝑉. 𝑠
= 9.12𝑥1014 /𝑠𝑒𝑐𝑜𝑛𝑑 = 9.12𝑥1014 𝐻𝑧
Assuming that the light is traveling in a vacuum, gives:
λ𝑚𝑎𝑥 =
𝑐
3.00𝑥108 𝑚/𝑠
=
= 3.29𝑥10−7 𝑚
𝑓𝑜 9.12𝑥1014 𝐻𝑧
e. This wavelength is 329nm, less than 400nm (violet) wavelength that marks the lower bound
of the visible spectrum. This light is beyond violet, and found in the ultraviolet region.
What’s More
Solve the following problems on the Photoelectric Effect. Show your solutions clearly.
1. A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20cm.
What is the energy of one photon of this microwave radiation?
Solution:
2. What is the maximum kinetic energy of an emitted electron if light with a frequency of
2𝑥1015 𝐻𝑧 shines on Aluminum with a Work Function ∅ = 4.08𝑒𝑉?
3. Given the Work Function for selenium is 5.11 eV.
a. What is the threshold frequency that is required to emit photoelectrons from Selenium?
b. A light with frequency of 3.56𝑥1015 𝐻𝑧 is utilized to illuminate the Selenium piece. What
would be the maximum kinetic energy of the ejected photoelectrons?
5
What I Can Do
The Photoelectric effect has numerous applications. Explore one application of this
Phenomenon utilized in your locality. Write your answer in a separate paper following the
given format below.
Application of Photoelectric Effect in the Society
Name of
Device/Apparatus
Location
Picture
6
Concept
Lesson
2
The Atomic Spectra
What’s In
In this lesson, you are going to study another phenomenon that was explained
using the particle-like behavior of light - the Atomic Spectra, specifically the absorption
and emission spectra. These phenomena are difficult to explain with classical physics
and were part of the body of evidence that pointed the way toward quantum
mechanics.
What I Need To Know
As you go along this lesson, you will be able to explain qualitatively the
properties of atomic emission and absorption spectra using the concept of energy
levels STEM_GP12MPIVh-46
What’s New
Atomic Spectra was explained using the concept of the Bohr Model of an atom
suggesting the quantization of energy.
From the word-box, Complete the diagram to review Bohr’s Model of an atom and have an
initial
understanding
on
the
Emission and Absorption spectra.
Write your answer in a separate
sheet.
electron
proton
nucleus
ground
absorbed
lowest
emitted
lower
level
excited
photon
light
7
What Is It
THE ATOMIC SPECTRA
When an object, whether solid, liquid or gas, is heated, they emit light. The emitted
light can be observed as a series of colored lines with dark spaces in between; this series of
colored lines is called a line or atomic spectra.
An Atomic Spectra is the spectrum of the electromagnetic radiation emitted or
absorbed by an electron during transitions between different energy level within an atom.
Atomic line spectra are another example of quantization. When atoms are excited, they emit
light of certain wavelengths which correspond to different colors.
There are three types of Atomic Spectra.
Type
Source
1. Continuous
Spectrum
A hot solid, liquid or
dense gas
2. Emission
Spectrum
A hot, rarified (lowpressured) gas
3. Absorption
Spectrum
A cool rarified (lowpressured) gas
Illustration
Line Spectra are either emitted or absorbed by
gases that are not dense. Each line corresponds to a
different wavelength and frequency. As shown in the
figure, the line spectra of the Hydrogen, Helium, Neon,
Sodium and Mercury are unique. No two elements have
the same spectra. Each element’s spectrum is a
“fingerprint” for that element. It can be used to identify the
element and its structure.
For example, in the given figure below, we can see
that elements D and Z are found in the mixture since their line spectra pattern are seen in the
mixture.
8
Emission and Absorption of a Photon
When a photon’s energy is absorbed
by the electron in an atom, the electron gets
excited and move from lower to higher
energy level. The photon must have the same
energy as the difference between the energy
levels in the atom or molecule.
When these electrons return to
ground state (lower energy level), they
radiate or emit energy in the form of
photons. The emission spectrum is formed
by the frequencies of these emitted photons.
Emission spectrum formed when the
electrons fall back down and leave the excited
state, energy is re-emitted in the form of
a photon and form different coloured lines in
the spectrum, whereas an absorption
spectrum has dark-coloured lines in or gaps
in the spectrum.
Neils Bohr and the Hydrogen Atom
The hydrogen atom is the simplest
atom because it has only one electron
orbiting its nucleus, showing four visible
colored lines in the spectrum.
Emission spectra were long been observed already for many other elements in the late
19th century. This observation presented a major challenge which cannot be explained in
classical physics. Thus the energy levels of a hydrogen atom had to be quantized.
Bohr’s Model of the atom is the 1st model that suggest that the energy of the electron
is quantized. The electrons exist in fixed orbits; that is the location and its energy are
quantized. His theory provides an adequate model in explaining the spectra.
The energies of the photons are quantized, and their energy is explained as being
equal to the change in energy of the electron when it moves from one orbit to another. In
equation form, this is
−𝑅ℎ𝑐
∆𝐸 = ℎ𝑓
and
𝐸𝑛 = 2
𝑛
Where
R = Rydberg constant
h = Planck’s constant
c = speed of light
n = positive integer corresponding to the number assigned to the orbit
9
In 1885, a Swiss mathematics teacher, Johann Balmer (1825–1898), showed that the
frequencies of the lines observed in the visible region of the spectrum of hydrogen fit a simple
equation that can be expressed as follows:
1
𝜆
where
and
= 𝑅[
1
22
−
1
𝑛2
]
n takes on values 3, 4, 5, and 6 for the four lines
R = 1.09737 × 107 m−1 is the Rydberg constant named after Johannes Robert
Rydberg, a Swedish physicist
The Balmer series extends into the UV region and ends at 365nm.
Later experiments found other series of lines in the UV and IR with patterns like the
Balmer series but at different wavelengths. The other spectral line series are named after their
discoverers, Theodore Lyman, A.H. Pfund, and F.S. Brackett of the United States and
Friedrich Paschen of Germany.
The Lyman series lies in the ultraviolet range containing lines with wavelength from
91nm to 122nm and its formula
1
𝜆
1
1
1
𝑛2
= 𝑅[ 2−
] where n = 2,3,…
Paschen’s series for the wavelength satisfies the formula
1
𝜆
1
1
3
𝑛2
= 𝑅[ 2−
]
where n = 4,5,6,…
A schematic of the hydrogen spectrum shows several series named for those who
contributed most to their determination. Part of the Balmer series is in the visible spectrum,
while the Lyman series is entirely in the UV, and the Paschen series and others are in the IR.
10
What’s More
Using the wavelength data of the elements given in the table, identify the
elements below by looking at their atomic spectra.
https://www.tamdistrict.org/cms/lib/CA01000875/Centricity/Domain/1483/Interpreting%20the%20EM%20Spectrum.pdf
What I Can Do
“How do astronomers use light to study stars and planets?”
Atomic Spectroscopy poses various applications in the vast field of Science. One of which is
in the field of Astronomy. Astronomers use light to study stars and planets. To understand
further the applications of Atomic Spectroscopy in this field, conduct a research on the latest
discovery of Astronomers and explain how the concept of atomic spectroscopy helped them
in their discovery. Write your answer in a separate paper following the template given.
Discovery
(include a cut-out of
the photo if available)
Discoverer
Date
11
Atomic
Spectroscopy
Concept
Reflection
Lesson
3
Radioactive Decay
What’s In
You have learned that an atom has electrons orbiting outside the nucleus. And
that the nucleus is made up of protons and neutrons.
However, some atoms have unstable nucleus. Elements with large number of
protons, or protons and neutrons combined, naturally have unstable nuclei. This
causes imbalance between the attractive nuclear forces and the repulsive electrical
forces and so it emits particles or waves to form a more stable atom. This process is
called radioactive decay.
This lesson will help you understand more how radioactivity occurs focusing on
the radioactive activity and half-life.
What I Need To Know
As you go along this lesson, you will be able to learn how to calculate
radioisotope activity using the concept of half-life STEM_GP12MPIVh-i-47
What’s New
Answer the following as directed to review your knowledge about radioactivity. Write
your answer in a separate paper.
In your OWN WORDS, define the following:
1. Radioactive Materials
2. Radioactivity
3. Half-Life
4. Radioactive Activity
12
5. The half-life period of a radioactive element is 100 days. After 400 days, one gm of the
element will be reduced to __________ gm.
a. 1/2
b. ¼
c. 1/8
d. 1/16
6. The half-life period of a radioactive substance is best determined by counting the number
of alpha particles emitted per second in a Geiger Muller counter from its known quantity. If
the half-life period of a radioactive substance is one month, then?
a. it will completely disintegrate in two months
b. l/8th of it will remain intact at the end of four months
c. 3/4th of it will disintegrate in two months
d. it will completely disintegrate in four months
7. An element with atomic mass number of 14 and atomic number 6 has how many neutrons?
a. 6
b. 8
c. 14
d. 20
8. Isotopes of an element have nuclei with
a. the same number of protons, but different numbers of neutrons.
b. the same number of protons, and the same number of neutrons.
c. a different number of protons, and a different number of neutrons.
d. a different number of protons, and the same number of neutrons.
9. If an atom's atomic number is given by Z, its atomic mass by A, and its neutron number by
N, which of the following is correct?
a. N = A + Z
b. N = Z – A
c. N = A - Z
10. What happens to the half-life of a radioactive substance as it decays?
a. It remains constant.
b. It increases.
c.It decreases.
What Is It
RADIOACTIVE DECAY
Radioactivity is the
phenomenon exhibited by the
nuclei of an atom as a result of
nuclear instability. It is the
spontaneous breakdown of an
atomic nucleus resulting in the
release of energy and matter
from the nucleus.
Some materials contain
unstable isotopes. This means
the nucleus is either too big to
hold itself together or has too
many protons or neutrons. In
order to become more stable,
they can decay by emitting some forms of radiation by an alpha particle, a beta particle or
gamma rays. These materials are called Radioactive. Unstable atoms continue to be
radioactive and undergo decay until they lose enough mass/particles that they become stable.
Radioactive decay happens randomly and one could not exactly tell when it would
occur. However, if there is enough sample of radioactive isotopes, we can determine the
activity rate of the sample and its half-life.
13
Radioactive Activity and Half-Life
1. Radioactive Activity, R - the number of decays taking place every second. In equation form,
𝑅=−
∆𝑁
∆𝑡
= 𝜆𝑁 ;
∆𝑁 = 𝑁 − 𝑁0
where
𝑁 = number of nuclei present at time t
𝑁0 = number of nuclei present at t = 0
𝜆 = the decay constant
The basic unit of activity is the becquerel (Bq) named after Henri Becquerel, the first
man to discover radioactive radiation.
1 𝐵𝑞 = 1 𝑑𝑒𝑐𝑎𝑦/𝑠𝑒𝑐
Another unit used in describing the Activity is the Curie (Ci) defined to be the activity
of 1 g of 226Ra, in honor of Marie Curie’s work with radium.
1𝐶𝑖 = 3.7𝑥1010 𝐵𝑞
2. Half-Life, 𝑇1/2 – the time required for the number of radioactive nuclei to decrease to ½ the
original number 𝑁0 of all the isotopes in the sample. The Half-life and the
decay constant are related by the equation:
𝑇1 =
2
0.693
𝜆
Another equation relating the half-life, 𝑇1 and Activity, 𝑅 can be expressed as:
2
𝑅=
0.693𝑁
𝑇1
2
If a radioactive sample contains N radioactive nuclei in some instant, we can solve for the
number of nuclei, ∆𝑁, that decays in time ∆𝑡, is proportional to 𝑁. This is given by the equation:
∆𝑁 = −𝜆𝑁∆𝑡
The number of nuclei present varies with time according to the equation:
𝑁 = 𝑁0 𝑒 −𝜆𝑡
where
𝑒 = 2.718
Sample Problem:
1. The half-life of a radioactive sample is 30minutes. If the sample originally contains
3𝑥1018 nuclei, how may of these nuclei remain after 2 hours?
14
Solution:
The half-life of the sample is 30minutes. In 2 hours, the number of half-life would be:
2ℎ𝑜𝑢𝑟𝑠
30𝑚𝑖𝑛
2ℎ𝑜𝑢𝑟𝑠
= 0.5ℎ𝑜𝑢𝑟𝑠 = 4 half-life periods
Thus, the remaining sample after 2hours is equal to:
1 1 1 1
1 4
17
18
18
( ) ( ) ( ) ( ) 𝑥 (3𝑥10 𝑛𝑢𝑐𝑙𝑒𝑖) = ( ) (3𝑥10 𝑛𝑢𝑐𝑙𝑒𝑖) = 1.875𝑥10 𝑛𝑢𝑐𝑙𝑒𝑖
2 2 2 2
2
2. The activity of a radioactive sample is 1.6 Ci and its half-life is 2.5 days. Then
activity after 10 days will be:
Solution:
The half-life of the sample is 2.5 days. To determine the number of half-life the sample
undergone:
10 𝑑𝑎𝑦𝑠
2.5 𝑑𝑎𝑦𝑠
= 4 half-life periods.
The initial activity of the sample is 1.6 Ci. The activity after 10 days will be
1 1 1 1
1 4
( ) ( ) ( ) ( ) 𝑥(1.6𝐶𝑖) = ( ) 𝑥 (1.6𝐶𝑖) = 0.1𝐶𝑖
2 2 2 2
2
3. It is estimated that the Chernobyl disaster released 6.0 MCi of 137Cs into the environment.
Calculate the mass of 137Cs released. (The half-life of 137Cs is 30.2 years)
Solution:
Recall your lessons in Chemistry.
One mole of a nuclide A𝑋 has a mass of 𝐴 grams, so that one mole of
137g. Using Avogadro’s number, 1 mole has 6.02×1023 nuclei. Thus,
𝑚=
137
Cs has a mass of
137𝑔𝑟𝑎𝑚𝑠
𝑥𝑁
6.02 × 1023 nuclei
Since the half-life 𝑇1 and Activity 𝑅 are given, we use the eq’n
2
𝑅=
0.693𝑁
𝑇1
to solve for
𝑁:
2
(𝑅) (𝑇1 )
𝑁=
2
0.693
=
(60𝑀 𝐶𝑖)(30.2 𝑦𝑒𝑎𝑟𝑠)
0.693
Converting Curies (Ci) to Becquerels (Bq) and years to seconds, we get
365𝑑𝑎𝑦𝑠 24ℎ𝑟𝑠 3600𝑠𝑒𝑐
3.7𝑥1010 𝐵𝑞
(60𝑥106 𝐶𝑖)(
)(30.2 𝑦𝑟𝑠)(
)(
)(
)
𝐶𝑖
1𝑦𝑟
1𝑑𝑎𝑦
1ℎ𝑟
𝑁=
= 3.1𝑥1026 𝑛𝑢𝑐𝑙𝑒𝑖
0.693
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Plugging this value to solve for the mass, we get:
𝑚=
137𝑔𝑟𝑎𝑚𝑠
𝑥(3.1𝑥1026 𝑛𝑢𝑐𝑙𝑒𝑖) = 70𝑥103 𝑔𝑟𝑎𝑚𝑠 = 70𝑘𝑔
6.02𝑥1023 nuclei
4. The initial mass of an Iodine isotope was 200g. Determine the Iodine mass after 30 days
if the half-life of the isotope is 8 days.
Solution:
𝑁 = 𝑁0 𝑒 −𝜆𝑡
𝜆=
The decay constant is equal to
0.693
𝑇1
2
𝑁 = 𝑁0 𝑒 −𝜆𝑡 = (200)𝑒
where
𝑇1
= 8𝑑𝑎𝑦𝑠
2
0.693(30)
8
= 200𝑒 −2.6 = 200𝑥0.074 = 14.9𝑔𝑟𝑎𝑚𝑠
−
What’s More
Solve the following problems on Radioactive Activity and Half-Life. Show your
solutions clearly.
1. Find the mass of a radioactive isotope if 3 half-lives occurred. The initial mass of the
material was 80g
2. Rex the dog died in 1750. What percentage of his original carbon-14 remained in 1975
when he was found by scientists? The half-life of carbon-14 is 5730 years.
3. You measure the beta decay activity of an unknown substance to be 5306Bq. 48 hours
later, the activity is 510Bq. What is the half-life in hours?
4. A certain container has 0.56grams of 90Sr. Calculate the activity of this material in units
of Curies. The half-life of 90Sr is 28.8 years.
5. A sample of protactinium-234 of mass 100 g has a half-life of of 6.7 hours.
A. What fraction of the sample has not decayed after 20.1 hours?
B. What is the mass of undecayed protactinium-234 after this period of time?
What I Can Do
List down at least 5 uses of radioactivity that is being utilized in our country.
16
Summary
The Photoelectric Effect
The photoelectric effect is a phenomenon in which electrons are ejected from the surface of a metal
when light is incident on it.
Photoelectric Effect was explained by Albert Einstein on the basis of Max Planck’s experiment on
blackbody radiation which suggested the particle-like nature of light.
The minimum energy needed for the electrons to escape is called the Work Function given by the
equation: ∅ = 𝐾𝐸𝑚𝑎𝑥 − 𝐸
where 𝐾𝐸𝑚𝑎𝑥 = 𝑒𝑉𝑜 .
𝑉𝑜, the stopping potential, is the voltage difference required to stop electrons from moving between
plates.
The Atomic Spectra
When an electron moves between different energy levels in an atom, an electromagnetic (EM) radiation
is emitted or absorbed. This spectrum of EM radiation is called the Atomic or Line Spectra.
Line spectra emitted or absorbed is unique to each element and is described as the ‘fingerprint’ for that
element. By looking at its line spectra, an unknown element can be determined.
The line spectrum of atomic hydrogen includes the Balmer series, the Lyman series and the Paschen
series. Scientists were able to describe the Atomic Spectra by using Bohr’s suggestion on the
quantization of the energy levels of electrons in an atom.
Radioactive Decay
Radioactivity is the phenomenon exhibited by the nuclei of an atom as a result of nuclear instability.
Radioactive decay happens randomly and one could not exactly tell when it would occur. However, if
there is enough sample of radioactive isotopes, we can determine the activity rate of the sample and
its half-life.
Radioactive Activity, R, refers to the number of decays taking place every second. In equation form,
∆𝑁
𝑅 = − = 𝜆𝑁
∆𝑡
Radioactive Activity can be expressed in units of Becquerel (Bq) or Curie (Ci) where
1 𝐵𝑞 = 1 𝑑𝑒𝑐𝑎𝑦/𝑠𝑒𝑐 and 1𝐶𝑖 = 3.7𝑥1010 𝐵𝑞
Half-Life, 𝑇1/2 refers to the time required for the number of radioactive nuclei to decrease to ½ the
original number 𝑁0 y of all the isotopes in the sample. The Half-life and the decay constant are related
by the equation: 𝑇1 =
2
0.693
𝜆
and in terms of the Radioactive Activity 𝑅 =
0.693𝑁
𝑇1
2
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Assessment: (Post-Test)
Multiple Choice. Answer the question that follows. Choose the best answer from the given
choices.
1. During Einstein’s Photoelectric Experiment, what changes are observed when the
frequency of the incident radiation is increased?
a. The value of saturation current increases
c. The value of stopping potential increases
b. The value of stopping potential decreases
d. No effect
2. How does the intensity affect the photoelectric current?
a. As intensity increases, the photoelectric effect increases
b. As the intensity increases, the photoelectric effect decreases
c. As the intensity decreases, the photoelectric effect becomes twice
d. No effect
3. On which part of the photoelectric cell does the radiation strikes?
a. Cathode
b. Anode
c. Ammeter
d. Radiation does not strike on the photoelectric cell
4. The photoelectric emission could be explained by the ____________
a. Wave nature of light
c. Particle nature of light
b. Dual nature of light
d. Quantum nature
5. A radioactive source has a half-life of 80 s. How long will it take for 7/8 of the source to
decay? a. 10 s
b. 70 s
c. 240 s
d. 640 s
6. What is the percentage of a 200g sample of Nitrogen-16 that decays to 12.5g in 21.6sec?
a. 12.5%
b. 6.25%
c. 25%
d. 100%
7. Thallium-208 has a half-life of 3.053min. How long does it take for 120g to decay to 7.50?
a. 21.12min
b. 6.106min
c. 48.84min
d. 12.21min
8. The graph shows how the radioactivity of a particular
isotope varies with time. What is the half-life of this
isotope?
a. 5 days
b. 10 days
c. 12.5 days
d. 2.5 days
9. Who is responsible for the model of the atom where
electrons travel in specific paths or orbits around the
nucleus?
a. Einstein
b. Bohr
c. Planck
d. Dalton
10. Atomic emission spectroscopy is
a. The measurement of intensity of emitted light at a particular wave length from the atoms that are
exited thermally.
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b. The measurement of absorbance of emitted light at a particular wave length from the atoms that
are exited thermally.
c. The measurement of intensity of emitted light at a particular wave length from the atoms that are
exited by monochromatic light.
d. The measurement of intensity of absorbed light at a particular wave length from the atoms that
are exited thermally.
11. What causes the emission of radiant energy that produces characteristic spectral lines?
a. gamma ray emission from the nucleus
b. return of electrons to lower energy levels
c. neutron absorption by the nucleus
d. movement of electrons to higher energy levels
For the following numbers, refer to the
given figure.
12. Which drawing represents the process
by which an emission line is formed?
13. Which drawing represents the process by which an absorption line is formed?
14. A composition of a crushed rock sample was
investigated using atomic spectroscopy. After
dissolving in acid, the rock sample solution
was
heated
to
produce
an
emission
spectrum. Shown below is this emission
spectrum, along with those of five metals.
Based on this spectral analysis, it can be
concluded that the rock sample contains
a. strontium and beryllium, but none of other three metals
b. all five of the metals
c. strontium, but none of the other four metals
d. none of the five metals
15. The diagram below shows possible transitions of electrons
between energy levels in an atom of a particular element.
Which transition would produce the line of shortest
wavelength on the absorption spectrum of the element?
a. Transition c
c. Transition d
b. Transition e
d. Transition a
19
Key to Answers
20
References
2021. Study.Com. https://study.com/academy/lesson/the-photoelectric-effect-physicslab.html.
2021. Physics.Bu.Edu.
http://physics.bu.edu/~duffy/EssentialPhysics/chapter27/section27dash3.pdf.
Caintic, Helen. 2018. General Physics 2 For Senior High School. 1st ed. Quezon City: C & E
Publishing, Inc.
Foundation, CK-12. 2021. "CK12-Foundation". CK-12 Foundation.
https://flexbooks.ck12.org/cbook/ck-12-physics-flexbook2.0/section/13.5/primary/lesson/photoelectric-effect-chem.
"GDPR". 2021. Byjus.Com. https://byjus.com/jee/photoelectric-effect/.
"Half-Life And Activity | Physics". 2021. Courses.Lumenlearning.Com.
https://courses.lumenlearning.com/physics/chapter/31-5-half-life-and-activity/.
Jadhav. 2021. "Photoelectric Effect Ppt". Slideshare.Net.
https://www.slideshare.net/santoshjadhav3110567/photoelectric-effect-ppt-42827361.
"NCI Dictionary Of Cancer Terms". 2021. National Cancer Institute.
https://www.cancer.gov/publications/dictionaries/cancer-terms/def/radioisotope.
Padua, Alicia, and Ricardo Crisostomo. 2005. Practical And Explorational Physics - Modular
Approach. 1st ed. Quezon City: Vibal Publishing House, Inc.
"PHOTOELECTRIC EFFECT". 2021. Powershow.
https://www.powershow.com/viewfl/78b0a7ODE2N/PHOTOELECTRIC_EFFECT_powerpoint_ppt_presentation.
"Photoelectric Effect - Principles Of Structural Chemistry". 2021. Sites.Google.Com.
https://sites.google.com/a/coe.edu/principles-of-structural-chemistry/relationshipbetween-light-and-matter/photoelectric-effect.
"Photoelectric Effect | Chemistry For Non-Majors". 2021. Courses.Lumenlearning.Com.
https://courses.lumenlearning.com/cheminter/chapter/photoelectric-effect/.
"Photoelectric Effect | Definition, Examples, & Applications". 2021. Encyclopedia Britannica.
https://www.britannica.com/science/photoelectric-effect.
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