Question

In photoelectric effect, the stopping potential \( V_0 \) vs frequency \( \nu \) curve is plotted. \( h \) is the Planck's constant and \( \phi_0 \) is the work function of metal. 
(A) \( V_0 \) vs \( \nu \) is linear. 
(B) The slope of \( V_0 \) vs \( \nu \) curve is \( \frac{\phi_0}{h} \). 
(C) \( h \) constant is related to the slope of \( V_0 \) vs \( \nu \) line. 
(D) The value of electric charge of electron is not required to determine \( h \) using the \( V_0 \) vs \( \nu \) curve. 
(E) The work function can be estimated without knowing the value of \( h \). 
Choose the correct answer from the options given below:

• A. (C) and (D) only
• B. (D) and (E) only
• C. (A), (B) and (C) only
• D. (A), (C) and (E) only

Hint:

In the photoelectric effect, the linear relationship between stopping potential and frequency is a result of the work function and Planck's constant. The slope of the curve is crucial in determining \( h \).

Answer 1

The Correct Option is C

The photoelectric equation is given by: \[ V_0 = \frac{h\nu}{e} - \phi_0, \] where: - \( V_0 \) is the stopping potential, - \( \nu \) is the frequency of incident light, - \( h \) is Planck's constant, - \( e \) is the charge of the electron, - \( \phi_0 \) is the work function. From this equation, we can see that \( V_0 \) is linear with respect to \( \nu \), with a slope of \( \frac{h}{e} \), and the intercept gives the value of \( \phi_0 \).

• (A) is true because the relation between \( V_0 \) and \( \nu \) is linear.
• (B) is also true because the slope of the line gives \( \frac{h}{e} \), and rearranging gives \( \frac{\phi_0}{h} \).
• (C) is true because the slope of the \( V_0 \) vs \( \nu \) line is related to \( h \).
• (D) is false because the value of the electric charge \( e \) is required to find \( h \) from the slope.
• (E) is false because to determine the work function, knowing \( h \) is essential, and the value of \( h \) cannot be determined from the \( V_0 \) vs \( \nu \) curve alone without knowing \( e \).

Final Answer: (3) (A), (B) and (C) only.