Quantum Physics

Question 1

The photoelectric effect.

Answer 1

The ejection of an electron from a metal surface when the surface is irradiated with electromagnetic radiation of a high enough frequency.

Question 2

Saturation Current.

Answer 2

All photoelectrons emitted per unit time reach all collector to give a maximum photocurrent. Since the number of emitted photoelectrons per unit time depends on the intensity of the radiation, the photocurrent will remain constant no matter how large V is made.

Question 3

Stopping potential.

Answer 3

The minimum potential difference to reduce the photoelectric current to zero. All the kinetic energy of the most energetic electron will be converted into electrical potential energy, eVs.

At this value of potential difference V, photocurrent JUST reached zero, where the electric field is strong enough such that even photoelectrons with greatest kinetic energy do not have sufficient energy to reach the collector and they are just turned back.

Question 4

The various observations/ evidence of the particulate nature of EM radiation.

Answer 4

Relevant observations include:
1. Emission of photoelectrons starts with no observable time lag, even for very low intensity of incident light, assuming the frequency f exceeds the threshold frequency.

2. For a given metal, no electron is emitted if the frequency of the radiation is below a certain threshold frequency Fo, even with high intensity of radiation. Above the threshold frequency, the maximum kinetic energy of the emitted electron increases linearly with the frequency of the radiation, even with low intensity of radiation.
3. Increasing the intensity of the radiation has no effect on the maximum energy of the electrons.

These observations provides evidence that the light transfers energy to the electrons in discrete amounts (“packets”) instead of a continuous transfer of energy (i.e. a wave) and the interactions between photons and electrons are one-to-one i.e. a single photon can only be absorbed by a single electron.

Question 5

The phenomenon which provides evidence for the wave nature of EM radiation.

Answer 5

Phenomena such as interference and diffraction provide experimental evidence that electromagnetic radiation is a wave.

Observation: When a monochromatic light is passed through a single slit followed by a double slit, a fringe pattern is produced on screen.

Explanation:

1. Diffraction at the single slit produces a point light source. Diffraction at the double slit produces 2 coherent light sources.
2. The bright lines on the screen are regions where constructive interference occurs. The dark lines are regions where destructive interference occurs.

These observations suggest that in its propagation through space, an electromagnetic wave behaves like a wave.

Question 6

Why there is a threshold frequency Fo for the photoelectric effect.

Answer 6

Each photon has an energy equals to the product of Planck constant and the frequency of the radiation.

Surface electron needs a minimum amount of energy to escape from the metal surface called the work function energy.

In order to emit the electron from the surface of metal, the photon must have an energy that is at least equal to the work function energy thus corresponding to a threshold frequency.

A single photon can only be absorbed by a single electron. Its energy cannot be split between electrons

Question 7

Why emitted electrons from a metal are likely to have a range of values of Kinetic energy for any one frequency of the electromagnetic radiation.

Answer 7

Electrons ejected from the surface of the metal and not making collisions with other metals atoms before escaping possess the maximum kinetic energy.

Many of the emitted electrons are involved in collisions on their way out of the surface and therefore emerge with energy which is less than the maximum.

Question 8

Why photoelectric current reaches saturation no matter how large potential difference is made.

Answer 8

When the V reach a large enough value, all photoelectrons emitted per unit time reach the gauze and give the maximum photocurrent.

Since the number of emitted photoelectrons per unit time depends on intensity, the photocurrent will remain constant no matter how large V is made.

Question 9

Why maximum photoelectric current increases with intensity of illumination/ EM radiation.

Answer 9

Greater intensity at a particular frequency means a greater number of photons per unit time absorbed, thus a greater number of photoelectrons are emitted per unit time and a greater photocurrent is produced.

Question 10

Why value of stopping potential Vs remains unchanged no matter how large the maximum photoelectric current is.

Answer 10

Stopping potential depends on the maximum kinetic energy of photoelectrons. The maximum Kinetic energy in turn depends on the energy of the photon and the work function energy.

Since these two variables remains constant, maximum KE and hence stopping potential is unchanged.

Question 11

Wave theory of light and the photoelectric effect.

Answer 11

1. Wave theory predicts that the photoelectric effect should occur for any frequency of the monochromatic incident light. If frequency of light is too low, its intensity can be increased to cause photoelectron emission.
2. Wave theory predicts that at very low intensities, there will be a time delay in Emission of Photoelectrons as the electrons would need time to accumulate sufficient energy in order to escape from the metal surface.
3. Wave theory predicts that if the incident light intensity is increased, a greater amount of energy will be incident on the surface and hence electrons will escape with more energy from the surface of the metal.

Question 12

Electron diffraction experiment

Answer 12

A potential difference accelerates the electrons to a momentum such that their de Broglie wavelength is in the same order of magnitude as the separation between atoms in the carbon films, which has lines in many directions due to its three dimensional structure.

Question 13

Explain the part played by diffraction in the production of concentric circles.

Answer 13

Electrons exhibit wave properties (Wave-particle duality) and spread/bend/ not diffract when they pass through the slits formed by the carbon film. The (electron) waves interfere constructively to form bright concentric circles on the screen.

Question 14

Explain how the existence of electron energy levels in atoms give rise to line spectra.

Answer 14

The energy levels are discrete, thus the difference between any two energy levels is discrete.
Only photons with energy equal to the difference in energies between any two levels will be absorbed or emitted. The energy of photon equals to hf.
Hence, the photons are of fixed frequencies, giving rise to line spectra, and not continuous spectra.

Question 15

Describe emission line spectra

Answer 15

A line spectra that consists of quite separate bright lines of definite wavelengths on a dark background and are given by luminous gases and vapours at low pressure.

Question 16

Describe absorption line spectrum

Answer 16

A continuous spectrum crossed by dark lines due to some missing frequencies and is produced when white light passes through a cooler gas or vapour.

Question 17

Describe absorption line spectrum

Answer 17

A continuous spectrum crossed by dark lines due to some missing frequencies and is produced when white light passes through a cooler gas or vapour.

Question 18

How does absorption line spectrum come about.

Answer 18

When unexcited gas atoms at low pressure absorbs photons from white light, they get excited and transit to a more excited state, provided the photon energies exactly matches the energy difference between the ground state and any higher levels.

This leads to absorption of only the photons with specific energies equals to hf, and hence specific frequencies. These photons are then re-emitted randomly in all directions.

The well defined and distinct dark lines in the spectrum correspond to the specific frequencies of light that are absorbed by atoms in the gas.

Question 19

How does emission line spectrum come about.

Answer 19

When free electrons are accelerated and collide with atoms of the gas at low pressure, the gas becomes hot and the electrons within the gas atoms become excited. Their electrons thus occupy higher energy levels.

During subsequent de-excitation to lower energy levels, the gas atoms emit photons of energies corresponding to the difference between the initial and final energy levels.

Since these energy levels are fixed, only photons of specific energies can be emitted. Resulting in a spectrum consisting of well defined and distinct coloured lines superimposed on a dark background which characterizes an emission line spectrum.

Question 20

How is the X-Ray spectra produced.

Answer 20

X-rays are produced when metal atoms are bombarded with high-energy electrons, which are accelerated using a high voltage supply.

Due to Braking radiation, where radiation is emitted when fast-moving electrons are rapidly slowed down as they pass through the electric field around an atomic nucleus, resulting in a continuous spectrum produced.

Question 21

How is characteristic X-Rays produced.

Answer 21

Characteristic X-rays are emitted when an electron in an upper state (L or M shell) of an atom falls to fill the vacated lower state (K shell) that has its electron dislodged by the bombarding electrons.

Patterns of characteristic X-rays is unique to each element.

Question 22

Describe the X-ray Spectra.

Answer 22

A spectrum consisting of a broad, continuous spectrum of radiation (due to braking radiation) with a cut-off wavelength (minimum wavelength), superposed on peaks of sharply defined wavelengths (Characteristic X-rays).

Question 23

Other features of the X-ray spectra.

Answer 23

Intensity of the X-ray spectra depends on:

(1) Energy of the X-ray photon
(2) Probability that X-ray photons of that particular wavelength will be produced.

A more energetic electron has a higher possibility of releasing more X-ray photons.

E.g. Although the M–>K transition produces a X-ray photon with higher energy than the L—>K one, the probability of the former occurring is significantly lower because the M-shell is further away from the K-shell.
Therefore, the K-Beta peak is lower than the K-Alpha peak and the wavelength of the K-Beta peak is smaller than that of the K-Alpha peak.

A higher probability of X-ray photon emission will shift the intensity-wavelength graph upwards.

Question 24

Features of the X-Ray spectra on the intensity-wavelength graph.

Answer 24

X-ray intensity depends on the number of electrons striking the target metal per unit time and the atomic number of the target metal.

When power input of the heater is increased, the rate of emission of electrons increases. Hence, intensity of X-ray increases. Energy of the each electron remains unchanged as the accelerating potential remains unchanged.

Higher accelerating potential results in electrons striking the target metal with higher kinetic energy. Therefore more interactions with the atomic nuclei / electrons of the target metal is possible before the electrons striking the target metal lose all their energy (i.e. more “braking radiation”), leading to an increase in the intensity of photons of all wavelengths emitted. Minimum wavelength only depends on the energy of the electrons.

For a metal with a different atomic number, the Kα and Kβ lines will be at a different wavelength. Minimum wavelength will remain the same. The wavelength of these characteristic x-rays is different for each element in the periodic table. The minimum wavelength is determined by energy of electrons and not dependent on target metal.

Question 25

Why is there a continuous distribution of wavelengths for X-ray spectra.

Answer 25

E.M. radiation (Photons) are produced whenever a charged particle is accelerated. The electrons hitting will have a distribution of acceleration, and hence wavelength.

Question 26

Why is there a sharp cut-off at short wavelength.

Answer 26

Minimum wavelength corresponds to the greatest acceleration of electrons. When all the energy of the electron with greatest Kinetic Energy has been converted into a single photon.