19 Quantum

Question 1

Definition of photoelectric effect

Answer 1

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

Question 2

How to tell if photoelectric emission has occurred at the emitter?

Answer 2

The ammeter registers a current due to the electrons from the emitter reaching the collector and completing the circuit.

Question 3

What is the purpose of adjusting the variable DC supply?

Answer 3

The potential of the collector is made more positive or negative with respect to the emitter to accelerate or decelerate the emitted electrons.

Question 4

Relationship between stopping potential and intensity of incident light

Answer 4

The two are independent.

Question 5

Relationship between photoelectric current and intensity of incident light

Answer 5

The two are proportional.

Question 6

Definition of a photon

Answer 6

A photon is a small discrete quanta of electromagnetic energy from a beam of light.

Question 7

Formula for energy of a single photon E

Answer 7

E = hf = hc/λ

Planck constant h = 6.63 x 10^-34
Electron-volt eV = 1.6 x 10^-19 (same as elementary charge)
E is proportional to f.

Question 8

Definition of work function Φ

Answer 8

The minimum amount of energy that will remove an electron from the surface of the metal.

Question 9

Formula for work function Φ

Answer 9

Φ = hf0 = hc/λ0

Question 10

Definition of threshold frequency f0

Answer 10

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

Note:
A photon’s energy cannot be shared among multiple electrons, one electron can only absorb one photon.

Question 11

Einstein’s equation for photoelectric effect (energy conservation)

Answer 11

E = Φ + Ekmax

Question 12

Definition of stopping potential Vs

Answer 12

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

Question 13

Formula for stopping potential, Vs

Answer 13

Ekmax = 1/2 mvmax^2 = eVs

Graph of stopping potential against frequency of incident light:
y = Vs
x = f
m = h/e
y-intercept = -Φ/e
x-intercept = f0

Question 14

Formula for intensity of incident radiation I

Answer 14

I = power/area = (energy/time)/area = [(Np/t)(hf)]/A = (Np/t)(hf/A)

Np/t = rate of photon arrival on metal surface

Question 15

Definition of saturation current

Formula for saturation current isat

Answer 15

At saturation current, all photoelectrons emitted will reach the collector

isat = Q/t = Nee/t = (Ne/t)e

Ne/t = rate of photoelectron emission from metal surface

Question 16

Explanation for existence of threshold frequency

Answer 16

Wave theory:
Photoelectric emission occurs for any frequency of monochromatic incident light.
Energy transfer is continuous, electrons accumulate energy until it has sufficient to escape.

Quantum theory:
Energy of incident photon must be larger than work function of metal for photoelectric emission to occur.
Increasing intensity of monochromatic incident light only increases number of photons arriving on metal surface per unit time, energy of each photon is not affected.

Question 17

Explanation for no time delay in emission of photoelectrons

Answer 17

Wave theory:
At low intensity light, there is less energy, electrons need time to accumulate sufficient energy to escape metal surface, causing time lag between emission of photoelectrons and incidence of light on surface.

Quantum theory:
For frequencies of incident photons more than threshold frequency of target metal, energy of photon is sufficient to overcome work function of metal to be ejected.
Photoelectrons are emitted immediately after light is incident on metal surface regardless of intensity.
Electrons cannot accumulate energy through absorption of multiple photons, each can only absorb one.

Question 18

Explanation for stopping potential independent of intensity of incident light

Answer 18

Wave theory:
Increasing incident light intensity causes greater amount of incident energy on surface, giving liberated electrons more energy.
Maximum kinetic energy possessed by ejected photoelectrons increases, stopping potential increases.

Quantum theory:
Increasing incident light intensity at constant frequency causes higher photon arrival rate.
Energy of each incident photon is unchanged.
Each photoelectron is liberated by one photon, maximum kinetic energy possessed by ejected photoelectron is unchanged, stopping potential is unchanged.

Question 19

Explanation for photocurrent proportional to intensity of incident light

Answer 19

Wave theory:
Intensity of wave is energy incident per unit area per unit time.
More incident energy liberates more electrons, increasing photocurrent.

Quantum theory:
Higher intensity of incident light of constant frequency causes greater number of photons arriving on metal surface per unit time.
More ejected photoelectrons per unit time, increasing photocurrent.

Question 20

Formula for de Broglie wavelength

Answer 20

λ = h/p = h/mv

Question 21

How does the existence of line spectra provides evidence for existence of discrete electron energy levels in isolated atoms

Answer 21

Each line on the line spectrum corresponds to a single wavelength, hence a single frequency of light
Energies of photons emitted are discrete
Since energy level of photons correspond to energy difference between two energy levels in an atom,
Energy levels of electrons within the atom are discrete as well

Question 22

Emission line spectrum

Answer 22

When a high potential difference is applied across a discharge tube containing the gas at low pressure the atoms of the gas are excited through inelastic collisions
Excited atoms are highly unstable and will quickly de-excite to lower energy states
Excited atoms emit photons while de-exciting

Question 23

Absorption line spectrum

Answer 23

White light consisting of photons of a continuous range of frequencies passes through a discharge tube containing the gas at low pressure and temperature
Photons which have the energies that correspond to the energy difference between two discrete energy levels are absorbed,
causing electrons to be excited from ground state to higher levels and subsequently de-excite, emmiting photons of similar energies to those absorbed randomly in all directions.
Hence the intensity of these photons is reduced, forming dark lines

Question 24

Heisenberg uncertainty principle

Answer 24

The heisenberg Uncertainty Principle states that it is impossible to measure the exact position and momentum at the same time

△x △p ≥ h