Question

Threshold frequency for a metal is \(15 \times 10^{14}\,\text{Hz}\). The light of wavelength \(6000\,\text{\AA}\) falls on the metal surface. Which one of the following statements is correct?
(Velocity of light, \(c = 3 \times 10^8\,\text{m/s}\))

• A. photoelectrons are emitted with velocity \(c\)
• B. photoelectrons come out with velocity \(3 \times 10^6\,\text{m/s}\)
• C. photoelectrons come out with zero velocity
• D. photoelectrons will not be emitted

Hint:

If incident light frequency is less than threshold frequency, no photoelectric emission occurs regardless of intensity.

Answer 1

The Correct Option is D

Step 1: Calculate frequency of incident light.
\[ \nu = \frac{c}{\lambda} \] \[ \lambda = 6000\,\text{\AA} = 6 \times 10^{-7}\,\text{m} \] \[ \nu = \frac{3 \times 10^8}{6 \times 10^{-7}} = 5 \times 10^{14}\,\text{Hz} \]

Step 2: Compare with threshold frequency.
Threshold frequency \[ \nu_0 = 15 \times 10^{14}\,\text{Hz} \] Incident frequency \[ \nu = 5 \times 10^{14}\,\text{Hz} \]

Step 3: Apply photoelectric condition.
Photoelectric emission occurs only if \[ \nu \ge \nu_0 \] Here, \( \nu<\nu_0 \).

Step 4: Final conclusion.
Since the frequency of incident light is less than the threshold frequency, photoelectrons will not be emitted.