Question

The maximum energy of photoelectron depends on __________.

• A. Threshold frequency of the metal
• B. Photoelectric work function of the metal
• C. Wavelength of the incident radiation
• D. All of these

Hint:

Kinetic energy of photoelectrons depends entirely on the *color/wavelength/frequency* of the light and the *material* of the target. It does completely NOT depend on the *intensity* (brightness) of the light.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the factors that dictate the maximum kinetic energy of electrons emitted during the photoelectric effect.
Step 2: Key Formula or Approach:
Albert Einstein's photoelectric equation mathematically relates these parameters: \[ K_{\text{max}} = h\nu - \Phi \] Where: $K_{\text{max}}$ = Maximum kinetic energy of the photoelectron $h\nu$ = Energy of the incident photon (which relates to its wavelength $\lambda$ since $\nu = c/\lambda$) $\Phi$ = Work function of the metal (which relates to threshold frequency $\nu_0$ since $\Phi = h\nu_0$)
Step 3: Detailed Explanation:
By substituting the alternative forms into Einstein's equation, we can write it in a few equivalent ways: 1. $K_{\text{max}} = \frac{hc}{\lambda} - \Phi$ 2. $K_{\text{max}} = h\nu - h\nu_0$ From these equations, we can clearly see that $K_{\text{max}}$ depends heavily on: - The wavelength ($\lambda$) or frequency ($\nu$) of the incident radiation. - The work function ($\Phi$) of the specific metal surface. - The threshold frequency ($\nu_0$), which is directly proportional to the work function. Since Options (A), (B), and (C) all represent parameters present in the fundamental equation determining $K_{\text{max}}$, the maximum energy inherently depends on all of them.
Step 4: Final Answer:
The maximum energy of the photoelectron depends on all of the listed factors.