In a photoelectric cell experiment, monochromatic light of frequency f and intensity I ill… — JAMB UTME

In a photoelectric cell experiment, monochromatic light of frequency $f$ and intensity $I$ illuminates a potassium surface, emitting photoelectrons with a stopping potential of $1.5\text{ V}$ . When the light frequency is increased to $1.5f$ and the intensity is set to $2I$ , the stopping potential rises to $3.5\text{ V}$ . What is the stopping potential if the light intensity is further increased to $4I$ while maintaining the frequency constant at $1.5f$ ?

$3.5\text{ V}$ Answer
B
$7.0\text{ V}$
C
$6.0\text{ V}$
D
$14.0\text{ V}$

Answer

3.5\text{ V}

According to Einstein's photoelectric theory, stopping potential

V_s

is directly proportional to maximum kinetic energy (

e V_s = hf - W_0

). It depends exclusively on the frequency of incident radiation and the target work function. Changing light intensity from

2I

4I

increases the number of emitted photoelectrons per second, but does not alter maximum kinetic energy. Therefore, at frequency

1.5f

, the stopping potential remains

3.5\text{ V}

Step-by-Step Solution

Identify the relationship between stopping potential, frequency, and light intensity in the photoelectric effect.

Einstein's photoelectric equation states that

e V_s = K_{\text{max}} = h f - W_0

, where

V_s

is stopping potential,

f

is frequency, and

W_0

is work function.

Stopping potential measures the maximum kinetic energy of emitted photoelectrons.

Analyze the impact of changing light intensity while holding frequency constant at

1.5f

Increasing intensity from

2I

4I

increases the number of incident photons per second (hence increasing emission current), but individual photon energy

E = hf

remains unchanged.

Photon energy depends solely on frequency

f

, not on radiation intensity.

Determine the new stopping potential value.

Since the frequency remains fixed at

1.5f

V_s

stays at

3.5\text{ V}

Maximum kinetic energy and stopping potential are independent of light intensity.

Key Concept

Independence of photoelectron kinetic energy and stopping potential from light intensity

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