Quantum Physics

Question 1

Define the photoelectric effect.

Answer 1

The photoelectric effect is the emission of photoelectrons from a metal surface when electromagnetic radiation of a sufficiently high frequency is incident on it.

Question 2

Define a photon.

Answer 2

It is a small discrete quanta of electromagnetic radiation. Its energy is the product of Planck’s constant and its frequency.

Question 3

Define the work function of a metal.

Answer 3

The work function of a metal is the minimum amount of energy that will remove an electron from the surface of the metal.

Question 4

Define threshold frequency f0.

Answer 4

The threshold frequency is the minimum frequency of an incident photon that will remove an electron from the surface of the metal.

Question 5

State Einstein’s Equation for photoelectric effect.

Answer 5

hf = Φ + eVs
f = frequency, Φ = work function, Vs = stopping potential

Question 6

Define stopping potential Vs.

Answer 6

The stopping potential is the minimum difference between the metal and collector that will prevent an ejected photoelectron from reaching the collector.

Question 7

Derive and state the formula for saturation current.

Answer 7

I = Q/t = Ne/t
Q = total charge, N = number of electrons, e = elementary charge

Question 8

Define ionisation energy and its formula.

Answer 8

Ionisation energy is the minimum energy needed to remove the outermost electron from an atom.

IE = ∣E∞ − Ei∣

Question 9

Define electron energy level.

Answer 9

It is the quantized energy corresponding to an allowed state of the electron within the atom.

Question 10

Describe the Bremsstrahlung effect (X ray production).

Answer 10

It is when a highly energetic electron is accelerated towards a heavy metal atom and loses some of its kinetic energy, and a X-ray photon is liberated.

Question 11

Define the Heisenberg Uncertainty and its formula.

Answer 11

It states that it is impossible to measure the exact position and momentum at the same time.
ΔxΔp ≥ h
Δx = uncertainty in position, Δp = uncertainty in momentum

Question 12

Describe what the emission line spectrum consists of.

Answer 12

The emission line spectrum consists of discrete bright coloured lines in a dark background.

Question 13

Describe what the absorption line spectrum consists of.

Answer 13

The absorption line spectrum consists of dark lines against a continous spectrum of the white light.

Question 14

Define the classical wave theory.

Answer 14

Classical wave theory considers light as a wave, which

involves continuous energy transfer which is dependent on the intensity of light.

Question 15

How does classical wave theory fail to explain the existence of a threshold frequency in photoelectric emission?

Answer 15

Wave theory predicts that photoelectric emission should occur for any frequency of the monochromatic incident light, since energy transfer is continuous, and the electron can accumulate energy until it has sufficient energy to escape.

In observation, no electrons were emitted at all unless the frequency of the monochromatic incident light
was higher than a minimum value (i.e. threshold frequency).

Question 16

How does quantum theory succeed in explaining the existence of a threshold frequency in photoelectric emission?

Answer 16

Quantum theory explains that in order for
photoemission to occur, energy of incident photon must be greater than work function of the metal (minimum energy required to liberate the atom from
the surface).

If frequency of the incident photon is less than threshold frequency of the target metal, incident photon has insufficient energy to cause emission.

Increasing intensity increases the number of photons arriving on the metal surface per unit time, but the energy of each photon remains insufficient to cause photoelectric effect.

Question 17

How does classical wave theory fail to explain no time delay in photoelectric emission?

Answer 17

Wave theory predicts that at very low intensities, there is a time lag between when the photoelectrons are emitted and when light is first incident on the surface.

Low intensity light has less energy and electrons would need time to accumulate sufficient energy in order to escape from the metal surface.

In observation, photoelectrons are emitted almost immediately with no appreciable time lag when the
metal is illuminated.

Question 18

How does classical wave theory fail to explain that stopping potential is independent of the intensity of incident light?

Answer 18

Wave theory predicts that increase in incident light intensity will cause a greater amount of energy to be incident on the surface and thus liberated electrons will
possess more energy.

The maximum kinetic energy that ejected photoelectrons possess should increase and the stopping potential should increase.

In observation, the stopping potential (indicative of the maximum kinetic energy of emitted electrons), is
independent of the incident light intensity at a constant frequency.

Question 19

How does classical wave theory fail to explain that photocurrent is proportional to intensity of incident light?

Answer 19

Wave theory predicts that since the intensity of a wave is the energy incident per unit area per unit time, more energy incident will result in a greater number of electrons liberated, thus a larger photocurrent.

In observation, the photocurrent (indicative of the number of photoelectrons emitted per second) is
proportional to the intensity of the light when the frequency is kept constant.

Question 20

How does quantum theory succeed in explaining no time delay in photoelectric emission?

Answer 20

Quantum theory explains that as long as the frequency of the incident photon is more than the threshold frequency of the target metal, the energy of the incident photon is sufficient to overcome the work function of the metal for it to be ejected.

Photoelectrons are emitted as soon as light is incident on the metal surface regardless of intensity. Each electron can only absorb one photon, thus an electron
cannot accumulate energy through absorption of multiple photons.

Question 21

How does quantum theory succeed in explaining that stopping potential is independent of the intensity of incident light?

Answer 21

Quantum theory explains that increasing the intensity at constant frequency causes a higher photon arrival rate. However, the energy of each incident photon remains the same.

Since each photoelectron is liberated by one photon, the maximum kinetic energy of the photoelectrons and hence stopping potential remains unchanged.

Question 22

How does quantum theory succeed in explaining that photocurrent is proportional to intensity of incident light?

Answer 22

Quantum theory explains that the higher the intensity of the incident light of constant frequency, the greater the number of photons arriving on the metal surface per unit time. More photoelectrons per unit time will hence be ejected, leading to a larger photocurrent.

Question 23

Use the concept of discrete electron energy levels to explain the existence of dark lines in an absorption spectrum.

Answer 23

Photons having energies that have the energy difference between two discrete energy levels are absorbed.

Electrons are excited from ground state to higher energy levels.

The excited atoms then return to their ground state by emitting photons of same energy in all directions.

Only part of this radiation is emitted in the same direction as the incident white light, thus there are dark lines in the absorption spectrum.

Question 24

Explain why there is a continous distribution of wavelengths in X-ray spectrum.

Answer 24

X-rays are produced when incident electrons are decelerated.

When incident electron collides with the metal atoms in the target, they lose an amount of their initial kinetic energy.

Different amount of their kinetic energies are lost in each collision, X-ray photons of various wavelengths are emitted, resulting in a continuous distribution of wavelengths.

Question 25

Explain why there are characteristic lines in an X-ray spectrum.

Answer 25

at that wavelength, electron in inner shell of target atom is excited on collision.

electron de-excites causing emission of a high intensity photon

discrete energy levels so discrete photon wavelengths with characteristic lines.

Question 26

Use the concept of discrete electron energy levels to explain the existence of coloured lines in an absorption spectrum.

Answer 26

When a high potential difference is applied across a discharge tube containing gas at low pressure, atoms of gas are excited through inelastic collisions.

Excited atoms are highly unstable and will quickly de-excite to lower energy states, emitting photons in the process

These photons have energies that correspond to the energy difference between any two discrete energy levels when the electrons de-excite.

Hence an emission spectrum consisting of coloured lines on a dark background is observed through the spectrometer. The different colours or frequencies are unique to the gas.