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Dual Nature of Radiation question

2013 · Shift 1 · Q59

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JEE Advanced
Physics
Dual Nature of Radiation
2013 · Shift 1 · Q59

Dual Nature of Radiation question

2013 · Shift 1 · Q59

JEE AdvancedPhysicsDual Nature of RadiationNumerical+3 / −1

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for silver to that of sodium is

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Numerical answer

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Correct answer: 1

For the photoelectric effect, Einstein’s equation is $eV_s = h\nu - \phi$ where:

$V_s$ = stopping potential
$\nu$ = frequency of incident light
$\phi$ = work function

Rearranging in terms of $V_s$ : $V_s = \frac{h}{e}\nu - \frac{\phi}{e}$
This is a straight-line equation of the form $V_s = m\nu + c$ so the slope is $m = \frac{h}{e}$
The slope depends only on fundamental constants $h$ and $e$ , and is independent of the metal used.
Therefore, for both silver and sodium, $m_{\text{Ag}} = \frac{h}{e}, \qquad m_{\text{Na}} = \frac{h}{e}$
Hence the required ratio is $\frac{m_{\text{Ag}}}{m_{\text{Na}}} = 1$

So, the work functions do not affect the slope; they only affect the intercept.

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