Graph shows variation of stopping potential with frequency of incident radiation on a metal plate. The value of Planck's constant is [ $e =$ charge on photoelectron]

Question

Graph shows variation of stopping potential with frequency of incident radiation on a metal plate. The value of Planck's constant is [ e = charge on photoelectron]

TestHub · Accepted Answer

According to Einstein's photoelectric equation:

$e V = h ν - Φ$

where $V$ is the stopping potential, $ν$ is the frequency of incident radiation, $h$ is Planck's constant, and $Φ$ is the work function of the metal.

From the given graph, we have two points $(ν_{1}, V_{1})$ and $(ν_{2}, V_{2})$ . Substituting these into the equation, we get:

$e V_{1} = h ν_{1} - Φ$

$e V_{2} = h ν_{2} - Φ$

Subtracting the first equation from the second, we obtain:

$e V_{2} - e V_{1} = h ν_{2} - h ν_{1}$

$e (V_{2} - V_{1}) = h (ν_{2} - ν_{1})$

Rearranging for Planck's constant $h$ , we get:

$h = \frac{e ( V _{2} - V _{1} )}{ν _{2} - ν _{1}}$

Answer: $\frac{e ( V _{2} - V _{1} )}{( ν _{2} - ν _{1} )}$

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