Introduction
Pada abad ke 19, ahli fizik begitu teruja dengan dua model yang mampu menjelaskan hampir kesemua
kaadaan fizikal dialam ini. Model tersebut ialah model zarah, yang yang dapat menjelaskan kaadaan jirim
dan model gelombang yang dapat menjelaskan tentang cahaya.
Cuma tinggal ialah usaha untuk menghubungkan kedua-dua model ini, dan jika ianya terhubung maka
ianya akan melengkapkan teori alam fizikal ini. Namun ianya tak semudah yang di jangkakan.
Pada penghujung abad ke 19 berlakulah sesuatu yang membingungkan ahli fizik secara keseluruhannya
apabila terjadinya ‘malapetaka ultraviolet’. Kaadaan ini terjadi apabila model gelombang (wave thoery)
tidak dapat menjelaskan fenomena sinaran jasad hitam(thermal radiation) dengan tepat.
Wave theory juga tidak dapat menjelaskan hasil eksperimen fotoelektrik.
Quantum Theory
To explain certain features of thermal radiation , Planck (in 1900) put forward the theory that energy
cannot be divided into smaller and smaller amounts. It is only emitted in discrete ‘packets’, each called a
quantum. The energy E of a quantum depends on the frequency f of the radiating source, as given by this
equation:
E = hf
where h is known as Planck’s constant. Its value, found by experiment, is 6.63 x 10 -34J s.
For electromagnetic radiation, c = fl, so the equation above can be rewritten as
,
where c is the speed of light and l the wavelength.
28.1 Photoelectric Effect
1. Figure shows a clean zinc plate placed on the cap of a gold-leaf electroscope. The electroscope is
given a negative charge so that the gold leaf diverges.
2. When the mercury lamp is switched off, the leaf stays in the same position. The mercury lamp is then
switched on, allowing ultraviolet radiation to be incident on the zinc plate.
3. The divergence of the gold leaf is observed to decrease. This divergence will stop if a glass plate is
placed between the zinc plate and the mercury lamp.
4. By placing the glass plate, the ultraviolet radiation is blocked. This has the same effect as switching off
the mercury lamp.
5. When ultraviolet radiation falls on the zinc plate, free electrons in the plate receive sufficient energy
and escape from the zinc plate.
6. The emission of electrons from the surface of a metal when light falls on it is called the photoelectric
effect. The emitted electrons are called photoelectrons.
7. If the electroscope is initially given a positive charge, the leaf remains in the same position even though
the mercury lamp is switched on. This is because the ultraviolet -radiation cannot supply enough energy
to the free electrons to escape from the positively charged zinc plate.
Photoelectric Effect
1. Figure shows a photocell circuit which can be used to study the photoelectric effect. A vacuum is
needed to prevent the collision of electrons with air molecules.
2. The cathode is coated with cesium. When monochromatic light of a certain frequency falls on the
cathode, photoelectrons are emitted.
3. The electric field set up between the anode and cathode by the battery causes the photoelectrons to be
attracted towards the anode.
4. These photoelectrons are detected as current by the galvanometer. The current is called photoelectric
current or photocurrent.
5. By fixing the distance of the monochromatic light source, its intensity can be kept constant.
6. The voltage across the anode and cathode is varied slowly using the potential divider. Figure 12.3
shows the graph of photoelectric current I against the voltage V applied between the anode and cathode.
7. As the voltage is increased, more photoelectrons are attracted to the anode. If the voltage is made
large enough, all photoelectrons emitted at the cathode are collected at the anode.
8. The current has now reached its limiting value. This current is known as the saturation current I s.
9. When V= 0, there is still current flowing in the circuit as there are still some photoelectrons with
sufficient energy arriving at the anode.
10. When the polarity of the voltage V is reversed, some photoelectrons would still reach the anode.
11. The flow of photoelectrons is stopped completely only when the reverse voltage V is large enough.
This reverse voltage required to stop the flow of photoelectrons is called the stopping potential V s.
12. When V = Vs the potential energy eVs equals the maximum kinetic energy Kmax of the photoelectrons.
The most energetic photoelectrons are stopped from reaching the anode.
where
e = charge of electron,
m = mass of electron and
vmax = maximum velocity of electron.
28.2 Concept of Light Quantisation
1. The following sections describe the features of the photoelectric effect. Features II,IV and V cannot be
explained using the wave theory of classical physics.
2. These features can only be explained using the concept of quantisation of light put forward by Einstein.
Feature I
1. If the frequency of the monochromatic light is fixed, the photoelectric current varies directly with the
intensity I for large values of V as shown in Figure.This means that more photoelectrons are emitted at
the cathode and collected at the anode.
2. Figure shows the graph of photoelectric current I against voltage V. Note that stopping potential V s is
independent of the light intensity.
Feature II
1. It is observed that photoelectrons are emitted only above a certain frequency of incident light for certain
metal surfaces.
2. The minimum frequency of the incident light required to eject the electrons from a metal surface is
called the threshold frequency or cut-off frequency fo. Different materials have different threshold
frequencies.
3. Below the threshold frequency fo, photoemission does not occur regardless of the light intensity. Figure
shows the different threshold frequencies for different materials.
4. The wave theory predicts that the photoelectric effect should occur for any frequency or intensity of
light. If the metal is exposed to the light long enough, the electrons will absorb sufficient energy to escape
from the metal surface, no matter how small the frequency or how low the intensity. However, this does
not occur.
5. Using the concept of quantisation of light, the energy of the light comes in discrete bundles called
quanta. These quanta of electromagnetic radiation are called photons. The energy of a single photon is
given by
E=hf
where
h = 6.63 x 10-34 J s (Planck’s constant) and
f = frequency of electromagnetic radiation.
6. If the frequency f of the radiation is less than the threshold frequency f o, then E < hfo. The energy E of
the photon would be insufficient to eject the electron from the metal surface. This feature is thus
explained by the concept of quantisation of light.
Feature III
1. If the intensity of the monochromatic light is kept constant, the stopping potential varies with the type of
material used.
2. Figure shows the graph of photocurrent I against frequency f for different materials.
Feature IV
1.The maximum kinetic energy Kmax of the photoelectrons increases as the frequency of the
monochromatic light increases, and is independent of the intensity of light.
2. Figure shows the graph of maximum kinetic energy Kmax against frequency f. Figure shows the plot of
photocurrent I against voltage V for different frequencies. Since Kmax = eVS, the stopping potential
Vs increases as the frequency f increases.
3. The wave theory predicts that the maximum kinetic energy should increase as the light intensity
increases. The electrons should gain more energy as a greater intensity means a greater amplitude of
radiation. However, this does not occur.
4. Using the concept of quantisation of light, the maximum kinetic energy increases only when the
frequency f of the radiation increases. Photons with greater energy E>hf o transfer more energy to the
electrons. Therefore, the photoelectrons can be ejected at a greater speed.
5. An increase in the intensity only means that more photons are absorbed, thereby ejecting more
electrons. However, the energy of each photon remains the same. Therefore, the maximum kinetic
energy of the photoelectrons is not affected by intensity. This feature is thus explained using the concept
of quantisation of light.
Feature V
1. If the frequency of the monochromatic light exceeds the threshold frequency fo, photoelectrons are
emitted almost immediately when the metal is illuminated.
2. The wave theory predicts that the photoelectrons are emitted only after a certain amount of time when
they have gained enough energy to escape from the metal. This contradicts actual results.
3. Using the concept of quantisation of light, when a photon of sufficient energy E ³ hfois absorbed by an
electron, the electron is immediately ejected from the metal surface. This feature is thus explained.
Contoh 1
Nyatakan perbezaan di antara thermionic emission and photoelectric emission.
28.3 Quantisation of Electromagnetic Radiation: Photons
1. In 1905, Einstein proposed that light is composed of discrete and concentrated bundles of energy,
called photons, travelling through space.
2. In other words, he proposed that light behaves not like a wave but like a particle. R. A. Millikan was
able to verify Einstein’s ideas in every aspect.
3. The. energy of each photon is given by
E=hf
where h = 6.63 x 10-31 J s (Planck’s constant) and
f = frequency of electromagnetic radiation.
Contoh 2
Calculate the energy in (a) joules and (b) kiloelectron-volt (keV) of a 0.45 nm photon.
[Speed of light in vacuum, c = 3.0 x 108 m s-1]
12.4 Work Function and Threshold frequency
The wave theory cannot explain the threshold frequency, or how low-amplitude waves can cause high-KE
electrons. Einstein’s quantum explanation Each photon delivers a quantum of energy, hf, which is
absorbed by an electron. Energy F is needed to free the electron from the surface. If hf is more than this,
the remainder is available to the electron as KE (though most electrons lose some KE before emission
because they interact with other atoms). So
Note:
• The number of electrons emitted is proportional to the number of photons absorbed.
• F is called the work function. Materials with a low F emit electrons in visible light. Those with a higher F
require the higher-energy photons of ultraviolet.
• If hf < F, no electrons are emitted.
• The energy of a photon at the threshold frequency = hf 0 = F . So, equation above can be rearranged and
rewritten:
Maul
Work function(eV)
Gold
5.1
Silicon
4.8
Iron
4.5
Aluminium
4.3
Silver
4.3
Contoh 3 :
An electromagnetic radiation of wavelength 300 nm is incident on a metal surface. The emitted electrons
have maximum kinetic energy of 1.10 x 10-19 J each. Calculate the lowest frequency required to remove
the electrons from the metal surface.
Relationship Between Stopping Potential and Frequency of Incident Radiation
1. Figure above shows a circuit set up to investigate the variation of the stopping potential V and the
frequency f of incident radiation.
2. A positive potential is applied to the plate A. The electrons that reach B will give the microammeter a
reading. Incident radiation of known frequency f is then directed towards plate A.
3. Using the potential divider, the potential of plate A is increased slowly until the microammeter reading
is zero.
4. This occurs because the increasing positive potential at A opposes the movement of the electrons from
A to B. As a result, the reading of the microammeter decreases.
5. When the potential of plate A equals the stopping potential VS, no more electrons reach B. In other
words, electrons with Kmax are completely stopped.
6. Points 3 and 4 are repeated using electromagnetic radiation of different frequencies.
7. A graph of V against f is plotted for a particular type of metal as shown in Figure 12.9.
8. Using Einstein’s photoelectric equation,
hf=Kmax+ F (1) When the microammeter reading is zero, Kmax = eV.
Equation (1) then becomes
hf=eVs+ F
eVS=hf-F
Therefore, the gradient for any metal =
9. The threshold frequency fo occurs when Kmax = 0, (that is VS = 0). Therefore, the intercept on the f-axis
gives the threshold frequency,fo. Using the value of fo, F can be calculated by F=hfo.
Contoh 4
When radiation of wavelength 184 nm is incident on a metal surface as shown in the figure, the
milliammeter reading falls to zero at a reverse voltage of 1.32 V.
What is the work function of the metal in electron-volt (eV)?