Atomic StructureHard

Question

A stationary He+ ion emitted a photon corresponding to the first line of the Lyman series. That photon liberated a photoelectron from a stationary hydrogen atom in the ground state. The velocity of the photoelectron is

Options

A.3.1 × 106 m/s
B.3.1 × 105 m/s
C.9.56 × 1012 m/s
D.9.56 × 106 m/s

Solution

K.E. of electron $= 13.6 \times 2^{2}\left( \frac{1}{1^{2}} - \frac{1}{2^{2}} \right) - 13.6 = 27.2\text{ eV}$

Now, $27.2 \times 1.6 \times 10^{- 19} = \frac{1}{2}9.1 \times 10^{- 31} \times v^{2}$

$v \approx 3.1 \times 10^{6}\text{ m/s}$

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