Question:
Sodium and Copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of their threshold wavelengths is nearly:
Sodium and Copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of their threshold wavelengths is nearly:
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A higher work function means electrons are tightly bound to the metal surface, requiring higher-energy photons (which correspond to shorter threshold wavelengths) to kick them out via the photoelectric effect.
Updated On: Jun 8, 2026
- 1:2
- 4:2
- 2:1
- 1:4
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The Correct Option is C
Solution and Explanation
Concept:
The work function \( \phi \) of a metal is inversely proportional to its threshold wavelength \( \lambda_0 \) according to Einstein's photoelectric equation:
\[
\phi = \frac{hc}{\lambda_0} \implies \lambda_0 \propto \frac{1}{\phi}
\]
Therefore, the ratio of the threshold wavelengths of two metals is equal to the inverse ratio of their work functions:
\[
\frac{\lambda_{01}}{\lambda_{02}} = \frac{\phi_2}{\phi_1}
\]
Step 1: Setting up the inverse work function ratio fraction.
From the question data:
• Work function of Sodium, \( \phi_1 = 2.3\,\text{eV} \)
• Work function of Copper, \( \phi_2 = 4.5\,\text{eV} \)
Applying the inverse relationship: \[ \frac{\lambda_{\text{Na}}}{\lambda_{\text{Cu}}} = \frac{4.5}{2.3} \]
Step 2: Evaluating the numerical value.
\[ \frac{4.5}{2.3} \approx 1.956 \approx 2 \] Thus, the ratio of their threshold wavelengths is very nearly \( 2:1 \).
Step 1: Setting up the inverse work function ratio fraction.
From the question data:
• Work function of Sodium, \( \phi_1 = 2.3\,\text{eV} \)
• Work function of Copper, \( \phi_2 = 4.5\,\text{eV} \)
Applying the inverse relationship: \[ \frac{\lambda_{\text{Na}}}{\lambda_{\text{Cu}}} = \frac{4.5}{2.3} \]
Step 2: Evaluating the numerical value.
\[ \frac{4.5}{2.3} \approx 1.956 \approx 2 \] Thus, the ratio of their threshold wavelengths is very nearly \( 2:1 \).
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