Question

The photons from Blamer series in hydrogen spectrum having wavelength between 450 nm to 700 nm are incident on a metal surface of work function 2 eV. Find the maximum kinetic energy of one photo electron.

Answer 1

a wavelength Range of (450-700)nm indicate an energy range of

$E=(1.78-2.76)ev.$

Now, a Balmer series transition emits energy of :-

$E=-13.6\times (\frac{1}{2^2}-\frac{1}{n^2})$ where n = 3,4,5 ...[Rydberg formula]

This given values, energy of photon as :-

$E=1.9,2.55,{2.856}^{\circ }....3.4ev$

so, only (1.9 & 2.55)ev is within the given Range. $\to \left(2\right)$

for photo emission energy of incident hight should be grater than

work function $\left(w_0\right)$ for metal. (Here $w_0=2ev)$.

clearly, only $E=2.55ev$ is permissible from (2).

so, Einsteins equation given max KE,

$K=E-w_0$

$=2.55-2=0.55ev$ (KE max of $e^{-})$