First slide

Bohr Model of the Hydrogen atom.

Question

Electrons from n=2 to n=1 in Hydrogen atom is made to fall on a metal surface with work function 1.2ev. The maximum velocity of photo electrons emitted is nearly equal to

Moderate

A

6 ×10⁵ m/s
B

3 ×10⁵ m/s
C

2 ×10⁵ m/s
D

18 ×10⁵ m/s

Solution

${KE}_{\max} = E - W_{o} ∴ \frac{1}{2} {mV}_{max}^{2} = 13 .6 z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) - W_{o} ∴ \frac{1}{2} \times 9 \times 10^{- 31} V_{max}^{2} = 13 .6 (1)^{2} (\frac{1}{1^{2}} - \frac{1}{2^{2}}) - 1 .2 eV ∴ \frac{1}{2} \times 9 \times 10^{- 31} V_{max}^{2} = [10 .2 - 1 .2] eV ∴ \frac{1}{2} \times 9 \times 10^{- 31} V_{max}^{2} = 9 \times 1 .6 \times 10^{- 19} ∴ V_{max} = 18 \times 10^{5} {ms}^{- 1}$

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