Case Study:

At a senior secondary school physics laboratory in Bengaluru, students perform an experiment to study the photoelectric effect, an important phenomenon that helped establish the quantum nature of light. The experiment uses an evacuated glass tube containing a photosensitive metal plate (cathode) and a collector plate (anode). When monochromatic light from a mercury lamp is directed onto the metal surface, electrons are emitted and a measurable current flows through the circuit. 

The students repeat the experiment with light of different frequencies while keeping the intensity constant. They observe that no electrons are emitted when the frequency is below a certain minimum value, known as the threshold frequency of the metal. Even if the light intensity is increased, no emission occurs below this frequency.

When the frequency exceeds the threshold value, electrons are emitted instantly. Increasing the intensity increases the photoelectric current because more electrons are emitted, but the maximum kinetic energy of electrons depends only on the frequency of the incident light, not its intensity. 

To measure the kinetic energy of emitted electrons, a reverse potential is applied between the plates. The negative potential at which the photocurrent becomes zero is called the stopping potential (V₀). At this point, even the most energetic electrons are unable to reach the collector plate. 

According to Einstein’s photoelectric equation:

K_max = hv - phi

where h is Planck’s constant, ν is the frequency of incident light, and φ is the work function of the metal. The stopping potential is related to kinetic energy as  eV₀ = K_max. 

By plotting stopping potential versus frequency, students obtain a straight-line graph whose slope equals h/e. This experiment not only confirms Einstein’s theory but also helps determine Planck’s constant experimentally.

Questions

Section A - MCQs

1. During the experiment, light of frequency lower than the threshold frequency is incident on the metal surface. What will happen?

A. Electrons will be emitted with low energy
B. Electrons will be emitted after some delay
C. No electrons will be emitted regardless of intensity
D. Only one electron will be emitted

2. In the photoelectric experiment, if the intensity of incident light increases while frequency remains constant (above threshold), what changes?

A. Maximum kinetic energy increases
B. Stopping potential increases
C. Number of emitted electrons increases
D. Threshold frequency changes

3. The stopping potential in the photoelectric experiment is used to determine:

A. Number of emitted electrons
B. Maximum kinetic energy of photoelectrons
C. Intensity of light
D. Wavelength of light

4. If the frequency of incident light increases, the stopping potential will:

A. Decrease linearly
B. Remain constant
C. Increase linearly
D. Become zero

Section B - Short Answer Questions

1. Why does increasing the intensity of light not increase the kinetic energy of photoelectrons?

2. Explain the concept of threshold frequency and its significance in the photoelectric effect.

3. A metal has a work function of 2.2 eV. If light of energy 3.0 eV is incident, calculate the maximum kinetic energy of emitted electrons.

Section C - Long Answer Question

1. During a photoelectric experiment, a metal surface with threshold frequency 5 × 10¹⁴ Hz is illuminated with light of frequency 8 × 10¹⁴ Hz.

a) Explain how the photoelectric effect occurs in this situation.
b) Using Einstein’s photoelectric equation, determine the maximum kinetic energy of emitted electrons if h = 6.63 × 10^-34 Js.
c) Predict what would happen if the light intensity is doubled while frequency remains the same.

Answer Key

MCQ Answers

1. C - No electrons are emitted if frequency is below threshold.
2. C - Higher intensity means more photons, so more electrons are emitted.
3. B - Stopping potential measures maximum kinetic energy.
4. C - Higher frequency increases electron kinetic energy and stopping potential.

Short Answer Solutions

1. Intensity only changes the number of photons striking the metal. The energy of each photon depends on frequency, so kinetic energy of emitted electrons remains unchanged.

2. Threshold frequency is the minimum frequency required to eject electrons from a metal surface. Below this value, photons do not have sufficient energy to overcome the work function.

3. Numerical

K_max = E_photon - phi
K_max = 3.0 eV - 2.2 eV
K_max = 0.8 eV

Long Answer Solution

a) Explanation

Since the incident frequency 8 × 10¹⁴ Hz is greater than the threshold frequency 5 × 10¹⁴ Hz, electrons are emitted from the metal surface.

b) Maximum kinetic energy

K_max = h(u - u₀)
= 6.63 × 10^-34 (8×10¹⁴ - 5×10¹⁴)
= 6.63 × 10^-34 (3×10¹⁴)
K_max = 1.989 × 10^-19 J

c) Effect of doubling intensity

• Number of emitted electrons increases
• Photoelectric current increases
• Maximum kinetic energy and stopping potential remain unchanged.