Physics Chapter 12

Question 1

State what is meant by the wavefunction of an electron. [1]

Answer 1

A measure of the probability of finding an electron at a particular place and time.

Question 2

Outline how fringes are formed when an electron beam is directed through a thin graphite crystal. [3]

Answer 2

When the electron beam is diffracted by the carbon atoms, path difference is formed between two layers of atoms. [1]
Due to the path difference, bright fringes are formed by constructive interference [1] and dark fringes are formed by destructive interference. [1]

Question 3

State what can be deduced about an electron from the amplitude of its associated wavefunction. [2]

Answer 3

The square of the amplitude of the wavefunction [1]
is the probability density of finding an electron at a particular place and time. [1]

Question 4

State Heisenberg uncertainty principle. [2]

Answer 4

It states that the position and momentum of a particle cannot be measured precisely simultaneously. [1]
When measuring a particle, the more precise is the position, the less precise is the momentum and vice versa. [1]

Question 5

Explain why photoelectrons are not emitted from the metal surface unless the frequency of incident light exceeds a minimum value. [2]

Answer 5

Photoelectrons are emitted only when the energy of the photon is larger than the work function. [1]
The energy of a photon is E = hf. The frequency of a photon has to be high enough such that the energy is greater than the work function. [1]

Question 6

State what is meant by the photoelectric effect. [1]

Answer 6

A phenomenon that photoelectrons are emitted when a metal surface is radiated by photons.

Question 7

An exact determination of the location of the electron in a hydrogen atom is not possible. Outline how this statement is consistent with the Schrödinger model of the hydrogen atom. [3]

Answer 7

Schrödinger model suggests the electron is described by a wavefunction ψ [1] which only gives a probability amplitude to find the electron at a particular place. [1]
Hence, the exact location of the electron is uncertain. [1]

Question 8

In the photoelectric effect experiment, the frequency of the light is reduced until the current measured by the ammeter falls to zero.
Explain how Einstein’s photoelectric theory accounts for this observation. [4]

Answer 8

According to Einstein’s photoelectric theory, light is considered as photons.
The energy of each photon is E = hf. [1]
Since the energy of a single photoelectron released from the metal comes from one photon, [1]
the current is reduced when the frequency of the light is reduced. [1]
When the energy is smaller than the work function of the metal, no photoelectrons is released. [1]
As a result, the current falls to zero.

Question 9

In the photoelectric effect experiment, light at a particular frequency is incident on a surface and electrons are emitted. Explain what happens to the number of electrons emitted per second when the intensity of this light is increased. [2]

Answer 9

The number of electrons emitted per second increases [1] because the number of photons increases when the intensity of the light is increased. [1]

Question 10

State what is meant by work function. [1]

Answer 10

The minimum energy needed to emit a photoelectron from the surface of a metal

Question 11

Outline how spectral lines are observed in the emission spectrum of hydrogen. [3]

Answer 11

The light emitted from a hydrogen discharge tube [1]
passes through a diffraction grating. [1]
The emission spectrum is then projected on a screen. [1]

Question 12

Explain how the emission spectrum of hydrogen gives evidence for the existence of discrete atomic energy levels. [3]

Answer 12

When the electron of the hydrogen atom transits from a higher energy level to a lower energy level, a photon is emitted. [1]
By E = hc/入, the wavelengths of the spectra correspond to the energies of the photon. [1]
Since only discrete wavelengths are observed, energy levels are also discrete. [1]

Question 13

The alpha particles and gamma rays produced in radioactive decay have discrete energy spectra. This suggests that nuclei also possess discrete energy levels. However, beta particles produced in radioactive decay have continuous energy spectra. Describe how the existence of the antineutrino accounts for the continuous nature of beta spectra. [3]

Answer 13

The total energy released is shared between the electron and electron antineutrino. [1]
The energy distribution of the electron and electron antineutrino is infinite. [1]
Hence, a continuous spectrum of beta decay is observed. [1]

Question 14

Monochromatic light is incident on a metal surface and electrons are emitted instantaneously from the surface. Explain why the emission of the electrons is instantaneous. [3]

Answer 14

The energy of each photon is E = hf. [1]
Since the energy of a single photoelectron released from the metal comes from one photon, [1]
the energy of the electrons does not accumulate. [1]
Electrons are emitted with no time delay.

Question 15

Monochromatic light is incident on a metal surface and electrons are emitted instantaneously from the surface. Explain why the energy of the emitted electrons does not depend on the intensity of the incident light. [2]

Answer 15

Intensity is a measure of the number of photons. [1]
The number of electrons emitted changes with the intensity instead of the energy of the electrons emitted. [1]

Question 16

Describe the de Broglie hypothesis. [2]

Answer 16

All particles have an associated wavelength [1] such that the de Broglie wavelength 入 = h / p, where h is Planck’s constant and p is the momentum of the particle. [1]

Question 17

Explain how the electron in a box model (of the hydrogen atom) gives rise to quantized energy levels. [3]

Answer 17

In the electron in a box model, the electron behaves as a standing wave in a box of size L, therefore L = n(入/2) where n = 1,2 … [1]
The wavelength of the electron is 入 = 2L / n. [1]
Therefore, the momentum and hence energy of the electron is quantized. [1]

Question 18

Explain how the electron in a box model (of the hydrogen atom) links with the Schrödinger model. [3]

Answer 18

Schrödinger model suggests that the electron in the hydrogen atom is described by a wavefunction. [1]
The energies of the electron in the standing waves are quantized. [1]
The square of the wave amplitude gives a probability density to find the electron at a particular place and time. [1]

Question 19

In 1924, Davisson and Germer carried out an experiment in which electrons were accelerated through a potential difference of 54 V. The electrons were scattered at the surface of a nickel crystal. Outline how the results of the experiment suggested that electrons exhibit wave properties. [2]

Answer 19

At certain angles, the intensity of the scattered electrons became maximum (=50°) and minimum. [1]
The maximum and minimum intensity were caused by the constructive and destructive interference respectively. [1]

Question 20

The photoelectric effect cannot be explained on the basis of a wave theory of electromagnetic radiation.
State two experimental observations, other than the existence of threshold frequency, that led to this conclusion. [2]

Answer 20

1. The maximum kinetic energy of the photoelectrons is independent of the intensity of the light.
2. The maximum kinetic energy of the photoelectrons depends on the frequency of the light and they are emitted instantaneously.

Question 21

Bohr modified the Rutherford model by introducing the condition mvr = nh/2π. Outline the reason for this modification.

Answer 21

Any 3 of the below:
* the electrons accelerate and so radiate energy
* they would therefore spiral into the nucleus/atoms would be unstable
* electrons have discrete/only certain energy levels
* the only orbits where electrons do not radiate are those that satisfy the Bohr condition