Photoelectric Effect: Doubling Frequency – Rankers Physics

Photoelectric Effects and deBroglie Equation: Practice Problem & Solution

Assertion (A): A metallic surface is irradiated by monochromatic light of frequency \(nu > nu_0\) (the threshold frequency). The maximum kinetic energy and stopping potential are \(K_{\text{max}}\) and \(V_s\) respectively. If the frequency of incident on the surface is doubled, both \(K_{\text{max}}\) and \(V_s\) are more than doubled. Reason (R): The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Photoelectric Effects and deBroglie Equation. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Photoelectric effect and linear dependence.
Formula: \(K_{\text{max}} = h\nu - h\nu_0\) and \(V_s = \frac{h\nu}{e} - \frac{h\nu_0}{e}\) where \(h\nu_0\) is the work function.
Solution: Both \(K_{\text{max}}\) and \(V_s\) are linearly dependent on frequency \(\nu\) with a positive slope and a negative intercept (work function term). Due to this negative intercept, if \(\nu\) is doubled, \(K_{\text{max}}\) and \(V_s\) will increase by more than double. Thus, both (A) and (R) are true, and (R) correctly explains (A).

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