Chp 18: Quantum

Question 1

define Photoelectric Effect:

Answer 1

The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when the incident electromagnetic radiation of frequency higher than the threshold frequency is incident on the surface.

Question 2

Observations of the Photoelectric Effect:

Answer 2

1) Existence of threshold frequency
2) Instantaneous emission of photoelectrons
3) Stopping potential is independent of intensity of incident EM radiation but dependent on frequency.

Question 3

define Photon:

Answer 3

A photon is a quantum of electromagnetic radiation whose energy, E is equal to hf, where h is the planck’s constant and f is the frequency of electromagnetic radiation.

Question 4

define Work function:

Answer 4

The work function of a metal is defined as the minimum amount of energy required for a free electron to escape from the surface of the metal.

Question 5

define Threshold frequency:

Answer 5

It is the minimum frequency of incident radiation required to cause the emission of photoelectrons from metal surface.

Question 6

define Ionization energy:

Answer 6

The minimum energy required to remove the outermost electron from the atom.

Question 7

define Heisenberg Uncertainty Principle:

Answer 7

It states that the product of the uncertainty of measurement of the position and momentum of a particle can never be smaller than the planck’s constant, h.

Question 8

Observation of Photoelectric Effect and how it proves that light behaves as Photons?

1. Existence of threshold frequency Wave Theory:

Answer 8

Even if frequency is low by E = Pt, the electrons should be able to accumulate sufficient energy given enough time then gets emitted regardless of the intensity or frequency of incident light, there should not be a minimum frequency.

Quantum Theory: Due to the 1 to 1 photon-electron interaction, the photon requires a minimum energy that is greater than the work function of the metal such that a photoelectron can be emitted from the metal surface. Hence if the photon has a smaller energy than the work function, the photoelectron will not be emitted. By E=hf, the frequency must be larger than a minimum frequency known as the threshold frequency.

Question 9

Observation of Photoelectric Effect and how it proves that light behaves as Photons?

2. Maximum kinetic energy and Stopping potential is independent of the intensity of incident EM radiation

Answer 9

Wave Theory: As intensity of light increases, the electron absorbs greater energy which should mean that the photoelectrons will be emitted with greater kinetic energy, hence the maximum kinetic energy of the photoelectrons should increase.

Quantum Theory: By increasing the intensity of incident radiation, this only increases the number of photons arriving at the metal surface per unit time. However, since E=hf, each photon still has the same energy, as such, due to the 1 to 1 photon-electron interaction, the electrons still absorb the same amount of energy from 1 photon, it should be emitted with the same maximum kinetic energy. However, more photoelectrons are emitted per unit time.

Question 10

Observation of Photoelectric Effect and how it proves that light behaves as Photons?

3. Instantaneous emission of electrons

Answer 10

Wave Theory: At low intensities, electrons would need a significant amount of time to accumulate enough energy before it gets emitted, there should be a measurable time-lag for the emission of electrons.

Quantum Theory: Due to the 1 to 1 photon-electron interaction, so long as the energy of photon is larger than the work function of the metal, the electrons should be emitted instantaneously regardless of the intensity of incident EM radiation.

Question 11

Why are photoelectrons emitted with a range of KE?

Answer 11

Electrons that are deep below the surface of the metal require additional work done against the interactions with the metal lattice as they collide with the metal lattice to be brought to the metal surface. The deeper the electrons, the lesser the KE they will be emitted with.

Question 12

Why for certain values of V, the photocurrent detected is zero?

Answer 12

When the values of V are below the stopping potential, even the photoelectrons with the most kinetic energy are unable to reach the collector as they experience a repulsive electric force. Since current is proportional to the rate of arrival of photoelectrons, no current is detected.

Question 13

State in terms of energy changes the required condition for electromagnetic radiation to cause electrons to be emitted from the surface of metal. (Photoelectric effect)

Answer 13

The energy of the incident photon must be larger than the work function of the metal. The difference between the energy of incident photon and the work function of the metal is the maximum kinetic energy of the photoelectrons emitted.

Question 14

Explain in terms of energy changes of the emitted photoelectrons, why there is a minimum potential difference (stopping potential) to reduce the photocurrent to zero.

Answer 14

There is a minimum potential difference as that is the potential difference which allows the electrons emitted with the most kinetic energy to convert all their kinetic energy to electrical potential energy just before reaching the collector. Since no electrons can reach the collector, there will be no current registered.

Question 15

Explain why the current does not continue to increase for positive values of potential difference in the photoelectric effect.

Answer 15

Saturation current occurs when all the emitted electrons reach the collector per unit time. Increasing the V after saturation current occurs does not change the number of electrons emitted per unit time from the emitter and hence the number of electrons per unit time arriving at the collector does not change and the current does not change.

Question 16

Observations to show the wave-particle duality:

1. Light behaves as a wave
2. Light behaves as particles
3. Electrons behave as particles
4. Electrons behave as a wave

Answer 16

1. Interference / Diffraction of light
2. Photoelectric effect
3. Electrons undergo collision, have mass and charge
4. Electron diffraction

Question 17

What is the difference in terms of exciting an electron to a higher energy level using collision of incident electrons vs absorption of photons?

Answer 17

Electron collision: When an incident electron has energy equal or higher than the energy level difference required for the transition, the incoming electron can transfer part of its KE to the bounded electron in the atom for it to transit to a higher energy level. The remaining energy (KE of incoming electron minus energy level difference of that transition) is then remained as KE of the incoming electron.

Photon absorption: When an incident photon has equal energy to the energy level difference of a transition, the bounded electron in the atom can absorb the photon then transit to a higher energy level. This process only works if the photon energy is exactly equal to the energy level difference of that transition. If not, the photon will not be absorbed at all.

Question 18

How an emission spectrum may be explained on the basis of the existence of discrete energy levels in atoms?

Answer 18

The coloured lines in the emission spectrum are clear and distinct with each line corresponding to a specific wavelength and frequency. As the electrons of an atom are at a higher excited state, it transits down, emitting a photon whose energy equals to the energy level difference of that transition. Since E=hf=hc/λ, since the energy levels are discrete, the photons emitted will have discrete energy hence discrete wavelengths.

Question 19

A beam of white light passes through a cold gas. Spectrum of dark lines occurs. Explain why these dark lines occur (Absorption spectrum)

Answer 19

White light consists of light of various wavelengths ranging from 400nm to 700nm. When the energy of an incoming photon matches the energy level difference of a particular transition, a photon will be absorbed, which excites the electron, the electron transits to a higher energy level. The photons which have energy that do not match the energy level differences of the gas will pass through to the diffraction grating, forming the coloured background. As the electrons de-excite, they will emit photons with energy equal to the energy level difference of that transition in random directions. Since the energy levels are discrete, by E= hc/λ, the photons emitted have discrete wavelengths and the intensity of these emitted photons are small relative to the original white light, which causes clear and distinct dark lines on the coloured background.

Question 20

Describe emission spectrum:

Answer 20

When a gas is heated or a potential difference is supplied to the gas, the electrons are excited, they transit to higher energy levels. As the excited electrons are unstable, they transit down to the lower energy levels, emitting a photon of energy equal to that of the energy level difference of that particular transition. Since the energy levels are discrete, the photons emitted have discrete energies, by E= hc/λ, thus discrete wavelengths. As the photons are incident on a diffraction grating, clear and distinct coloured lines will be formed on a dark background.

Question 21

Describe the appearance of a visible line emission spectrum.

Answer 21

Clear and distinct coloured lines on a dark background.

Question 22

How does the line spectra provide evidence for discrete energy levels in isolated atoms?

Answer 22

Excited electrons in the atom transit down, emitting photon of energy equal to that of the energy level difference of that transition. Since clear and distinct lines are seen with each line corresponding to a specific wavelength, this implies that the photons have discrete wavelengths, E=hc/λ, the photons have discrete energies. Therefore, this implies that the energy level difference in the gas atoms is discrete, hence the energy levels in the gas atoms are discrete.

Question 23

Explain the origins of continuous spectrum, characteristic lines and cut-off wavelength in X-ray production.

Answer 23

Continuous spectrum: The incoming electron with high KE interacts with the target atom and decelerates, it produces an X-ray photon of energy equal to the kinetic energy lost by the incident electron due to braking radiation. After the interaction, the electron can undergo subsequent interaction with the target atoms again, undergoing different decelerations hence producing X-ray photons of different energies hence wavelengths.

Characteristic lines: When the incoming electron has sufficient energy, it can knock out a deep-lying inner shell electron from the target atom, leaving a vacancy. Electrons from outer shells can undergo a downward transition to achieve stability, emitting an X-ray photon of energy equal to that of the energy level difference of that transition.

Minimum wavelength: When the electron interacts with the target atom and comes to a stop, it transfers all of its KE into the energy of the X-ray photon emitted. Hence the minimum wavelength corresponds to the maximum energy of the X-ray photon emitted. (E=hc/λ)

Question 24

In X-ray production, suggest 2 important properties of the materials used for the cathode (the filament) and the target.

Answer 24

Cathode:
1. A low value for its work function so that electrons can escape from its surface easily.
2. A low heat capacity so that less heat is required to raise its temperature.

Target:
1. A high melting point to withstand the large amounts of heat produced when electrons bombard it.
2. Has high atomic number so that it is more efficient in the production of X-rays,
3. A good conductor of heat so that heat can be removed from it easily.

Question 25

In X-rays why is Kβ a shorter wavelength than Kα?

Answer 25

A Kα transition is from the L-shell to the K-shell while the Kβ transition is from the M-shell to the K-shell. Since the energy level difference between K and M is more than K and L, the photon emitted from a Kβ transition will have higher energy as the energy of the photon emitted equals to the energy level difference of the transition, thus by E=hc/λ shorter wavelength.

Question 26

In X-rays why is the intensity for Kβ lower than Kα?

Answer 26

Intensity of the Kα line is relatively higher than that of the Kβ line because the rate of emission of Kα photons is greater than the rate of emission of Kβ photons. This is because the electrons in the L-shell are closer to the K-shell, hence there is a greater probability that the vacancy in the K-shell is filled by an electron from the L-shell than from the M- shell.

Question 27

Describe and explain the changes to the X-ray graph if the following modifications are made separately.

Answer 27

1. The temperature of the cathode is increased by increasing the current in the cathode: When the temperature of the cathode is increased, the rate of emission of electrons from the cathode increases, the rate of collision of electrons with the target increases, the rate of emission of X-ray photons increases, the intensity of the X-rays increases for all wavelengths, but the minimum wavelength, λmin and the wavelengths of the characteristic X-rays remain unchanged as the same metal is used.
2. When accelerating pd is increased: λmin decreases as λmin =hc/q∆V, since pd increases. The intensity of all wavelengths increases because the speed of the electrons increases, the rate of collision of electrons with the target increases, more X-rays photons produced per second, the wavelengths of the characteristic X-rays remain unchanged as the same metal is used.

Question 28

What is the meaning of radiation pressure?

Answer 28

When a photon is reflected off a surface it experiences a change in momentum as photons have momentum given by p=h/λ. By N2L, there is a force exerted by the surface on the photons. By N3L, there is an equal and opposite force exerted by the photons on the surface. Since pressure = force/area, the photons cause radiation pressure.

Question 29

Describe electron diffraction.

Answer 29

When electrons are incident on a graphite film, the de-Broglie wavelength of the electrons are approximately the same order of magnitude as the distance between carbon atoms in the graphite layer. They undergo diffraction, forming bright fringes of concentric rings as they hit the fluorescent screen.

Question 30

In electron diffraction, when the accelerating potential difference is increased, what change will be observed on the screen?

Answer 30

As the electrons lose more EPE, they gain more KE, hence the electrons attain a higher speed hence greater momentum. By p=h/λ the de-Broglie wavelength of the electrons decreases, by dsin θ = nλ, the electrons will have a lesser angle of diffraction and hence the diameter of the concentric rings decreases.

Question 31

Why is the energy level negative?

Answer 31

The electrostatic force on the electron in the atom is attractive, the highest possible energy level is defined to be zero and positive work done is required to cause the electrons to transit to a higher energy level.

Question 32

define stopping potential

Answer 32

minimum retarding potential to stop all the electrons from reaching the collector

Question 33

Give 2 reasons why photoelectrons emitted per sec/photons incident per sec is less than 1

Answer 33

• most photons are reflected from the metal surface
• atoms are made up of majority empty space and thus the probability of a photon hitting a surface electron is very small
• electrons at a deeper level which recelieve the photon energy will lose the enerygy when colliding the ion lattice or when colliding with other electrons

Question 34

the work fun of a certain metal in air increases over time. why

Answer 34

metal surface gains an oxide layer over time. electrons will require more energy to escape by photoelectric emission from the surface`