Question

If the energy of H-atom in the ground state is $-E$, the velocity of photo-electron emitted when a photon having energy $E_p$ strikes a stationary $L{i}^{2+}$ ion in ground state, is given by:

• A. $v=\sqrt{\frac{2(E_p-E)}{m}}$
• B. $v=\sqrt{\frac{2(E_p+9E)}{m}}$
• C. $v=\sqrt{\frac{2(E_p-9E)}{m}}$
• D. $v=\sqrt{\frac{2(E_p-3E)}{m}}$

Answer 1

Answer: (C)

$v=\sqrt{\frac{2(E_p-9E)}{m}}$

The energy of the atom in a particular shell\propto $Z^2$. Hence ground state energy of Li ion=-3^2E_1=-9E_1

Work function for $L{i}^{2+}=9E$
(ground level energy)

$E_p=w+\frac{1}{2}m{v}^2$; $E_p=9E+\frac{1}{2}m{v}^2$
$v=\sqrt{\frac{2(E_p-9E)}{m}}$

Hence, the correct option is $C$