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 \( h \). \text{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 defined as: \[V_0 = \frac{hu}{e} - \phi_0,\] where: - \( V_0 \) represents the stopping potential. - \( u \) denotes the frequency of the incident light. - \( h \) is Planck's constant. - \( e \) signifies the electron's charge. - \( \phi_0 \) is the work function. This equation demonstrates a linear relationship between \( V_0 \) and \( u \). The slope of this linear relationship is \( \frac{h}{e} \), and the intercept corresponds to the work function \( \phi_0 \). - Statement (A) is accurate because the relationship between \( V_0 \) and \( u \) is linear. - Statement (B) is also accurate. The slope of the line is \( \frac{h}{e} \). Rearranging this yields \( \frac{\phi_0}{h} \). - Statement (C) is correct because the slope of the \( V_0 \) versus \( u \) graph is directly related to Planck's constant \( h \). - Statement (D) is incorrect. The value of the electron's charge \( e \) is necessary to determine \( h \) from the slope. - Statement (E) is incorrect. Determining the work function requires knowledge of \( h \). However, \( h \) cannot be calculated solely from the \( V_0 \) versus \( u \) curve without knowing the value of \( e \). Final Answer: (3) (A), (B) and (C) only.