Balancing Nuclear Equations
Sample Problem 1
Write an equation for the emission of an alpha particle from 226
88Ra.
Sample Problem 2
Write an equation for the emission of a beta particle from 214
82Pb.
3. Write a balanced nuclear equation for the radioactive decay of
thorium-230 with the emission of an alpha particle.
4. Write an equation for the beta decay of thorium-231.
5. Write an equation for the beta decay of 93
38 Sr.
6. A 214
84 Po nucleus emits an alpha particle, followed by the emission of
a beta particle. Write two nuclear equations to illustrate the two consecutive
reactions.
Atomic Theories: Bohr and Quantum Theory
Understanding Concepts
1. State the two important experimental observations that
established the quantum theory of light.
2. Although Einstein received the Nobel Prize for his explanation
of the photoelectric effect, should Max Planck be considered
the father of quantum theory?
3. Write a brief description of the photoelectric effect experiment.
4. Distinguish between the terms “quantum” and “photon.”
Applying Inquiry Skills
5. What effect does the type or colour of light have on the
release of electrons from a sodium metal surface?
(a) Write a brief experimental design to answer this question,
based on Figure 6. Be sure to identify all variables.
(b) Would you expect all colours of light to release electrons
from the sodium metal? Justify your answer, in
general terms, using the idea of photons.
Extension
6. Einstein won the Nobel Prize in 1921 for explaining the
photoelectric effect in 1905. Einstein calculated the energy
of an incoming photon from the Planck equation
E _ hf
where E is energy in joules (J), h is Planck’s constant
(6.6 x 10–34 J/Hz), and f is the frequency in hertz (Hz) of
light shining on the metal.
(a) If the minimum frequency of light required to have an
electron escape from sodium is 5.5 _ 1014 Hz, calculate
the energy of photons of this frequency.
(b) What is the minimum energy of the quantum leap that
an electron makes to escape the sodium atom as a
photoelectron?
7. Ultraviolet (UV) light that causes tanning and burning of
the skin has a higher energy per photon than infrared (IR)
light from a heat lamp.
(a) Use the Planck equation from the previous question to
calculate the energy of a 1.5 _ 1015 Hz UV photon and
a 3.3 _ 1014 Hz IR photon.
(b) Compare the energy of the UV and IR photons, as a
ratio.
(c) From your knowledge of the electromagnetic spectrum,
how does the energy of visible-light photons and X-ray
photons compare with the energy of UV and IR
photons?
Quantum Numbers
Understanding Concepts
1. What is the main kind of evidence used to develop the
description of electrons in terms of quantum numbers?
2. Briefly, what is the theoretical description of electrons in
atoms provided by each of the four quantum numbers?
3. Each value of the secondary quantum number is used to
determine the possible values of the magnetic quantum
number.
(a) How many possible values of ml are there for
l _ 0, 1, 2, and 3?
(b) What pattern do you notice in these numbers?
(c) Using your answer to (b), predict the number of possible
values of ml for l _ 4.
4. Theoretical knowledge in science develops from a need to
explain what is observed. What is the fourth quantum
number and why is it necessary?
5. Using Table 4 as a guide, complete the next section of this
table using n _ 4.
6. How many quantum numbers does it take to fully describe
an electron in an atom? Provide an example, listing labels
and values of each quantum number.
Electron Configurations
Understanding Concepts
3. Complete electron energy-level diagrams for the
(a) phosphorus atom
(b) potassium atom
(c) manganese atom
(d) nitride ion
(e) bromide ion
(f) cadmium ion
6. Identify the elements whose atoms have the following electron configurations:
(a) 1s2 2s2
(b) 1s2 2s2 2p5
(c) 1s2 2s2 2p6 3s1
(d) 1s2 2s2 2p6 3s2 3p4
7. Write full electron configurations for each of the Period 3 elements.
8. (a) Write shorthand electron configurations for each of the halogens.
(b) Describe how the halogen configurations are similar. Does this general pattern
apply to other families?
Understanding Concepts
1. Determine the maximum number of electrons with a principal
quantum number
(a) 1 (c) 3
(b) 2(d) 4
3. State the aufbau principle and describe two methods that
can be used to employ this principle.
4. If four electrons are to be placed into a p subshell, describe
the procedure, including the appropriate rules.
5. (a) Draw electron energy-level diagrams for beryllium,
magnesium, and calcium atoms.
(b) What is the similarity in these diagrams?
6. The last electron represented in an electron configuration
is related to the position of the element in the periodic
table. For each of the following sections of the periodic
table, indicate the sublevel (s,p,d,f) of the last electron:
(a) Groups 1 and 2
(b) Groups 3 to 1 2(transition metals)
(c) Groups 13 to 18
(d) lanthanides and actinides
7. (a) When the halogens form ionic compounds, what is the
ion charge of the halide ions?
(b) Explain this similarity, using electron configurations.
8. The sodium ion and the neon atom are isoelectronic; i.e.,
have the same electron configuration.
(a) Write the electron configurations for the sodium ion
and the neon atom.
(b) Describe and explain the similarities and differences in
properties of these two chemical entities.
9. Use electron configurations to explain the common ion
charges for antimony; i.e., Sb3_ and Sb5_.
10. Predict the electron configuration for the gallium ion, Ga 3_.
Provide your reasoning.
11. Evidence indicates that copper is paramagnetic, but zinc is
not. Explain the evidence.
12. Predict the electron configuration of a gold atom. Provide
your reasoning.
13. Use electron configurations to explain the
(a) 3_ charge on the scandium ion
(b) 1_ charge on a silver ion
(c) 3_ and 2_ charges on iron(III) and iron(II) ions
(d) 1_ and 3_ charges on the Tl1_ and Tl3_ ions
14. Carbon, silicon, and germanium all form four bonds. Explain
this property, using electron configurations.
Wave Mechanics and Orbitals
Understanding Concepts
1. Briefly state the main contribution of each of the following
scientists to the development of quantum mechanics:
(a) de Broglie
(b) Schrödinger
(c) Heisenberg
2. What is an electron orbital and how is it different from an
orbit?
3. State two general characteristics of any orbital provided by
the quantum mechanics atomic model.
4. What information about an electron is not provided by the
quantum mechanics theory?
5. Using diagrams and words, describe the shapes of the 1s,
2s, and three 2p orbitals.