The Question is from neet-physics dual-nature-matter-radiation einsteins-photo-electric-equation, and it was created by the author ABDUL JILANI BASHA

Question

A metal surface is illuminated by light of frequency $2
u_0$, where $
u_0$ is the threshold frequency.  If the intensity of the light is doubled, the maximum kinetic energy of the emitted photoelectrons will:

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
 **Primary Concept**: Photoelectric effect
 **Related Topics**: Quantum nature of light, work function, kinetic energy
 **Prerequisites**: Understanding of Einstein's photoelectric equation.
## SOLUTION PATHWAY
**Given Information**:
  Frequency of incident light: $2
u_0$
  Threshold frequency: $
u_0$
  Intensity of light is doubled.
  
**Method & Steps**:
 1. Apply Einstein's photoelectric equation:
  Reasoning: The maximum kinetic energy of emitted photoelectrons is related to the frequency of incident light and the work function of the metal.
  Formula/Rule: $KE_{max} = h
u - \phi$, where $KE_{max}$ is the maximum kinetic energy, $h$ is Planck's constant, $
u$ is the frequency of incident light, and $\phi = h
u_0$ is the work function.
 2. Substitute given values:
  Working: $KE_{max} = h(2
u_0) - h
u_0 = h
u_0$
  Key Point: The maximum kinetic energy depends only on the frequency of the incident light and the work function, not on the intensity.
 3. Analyze the effect of doubling the intensity:
  Reasoning: Doubling the intensity increases the number of photons, but not the energy of individual photons.  Therefore, the maximum kinetic energy of the emitted electrons remains unchanged.
  Result: $KE_{max} = h
u_0$ (remains unchanged)
  Verification: The equation shows that $KE_{max}$ is independent of intensity.
 ## OPTION ANALYSIS
A :x: Doubling the intensity increases the number of photons, not the energy of each photon.  Therefore, the maximum kinetic energy doesn't double.
B :x:  The maximum kinetic energy is not halved; it remains the same.
C ✓: The maximum kinetic energy depends only on the frequency of the incident light and the work function, which are unchanged when intensity is doubled.
D :x: There is no factor of $\sqrt{2}$ involved in the change of maximum kinetic energy.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing intensity with energy of photons: Intensity is the number of photons, while energy depends on frequency.
  How to avoid: Remember that $E = h
u$, where E is the energy of a single photon.
  2.Ignoring the work function: The work function is crucial in determining the maximum kinetic energy.
  How to avoid: Always include the work function ($\phi$) in the photoelectric equation.
 **Quick Tips**:
  1.Focus on the photoelectric equation to solve problems related to the photoelectric effect.
  2.Remember that intensity affects the number of emitted electrons, not their maximum kinetic energy.

ABDUL JILANI BASHA · Answer

Double

ABDUL JILANI BASHA · Answer

Halve

ABDUL JILANI BASHA · Answer

The correct Option is "Remain unchanged"

ABDUL JILANI BASHA · Answer

Increase by a factor of $\sqrt{2}$

NEET Physics Dual Nature of Matter and Radiation Einsteins Photo Electric Equation MCQs

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