Question

An electron in ground state absorbs 1.5 times as much energy required for its escape from H atom. The wavelength the electron emitted in A${}^o$ is:

• A. $2.30A^o$
• B. $4.71A^o$
• C. $10A^o$
• D. None of these

Answer 1

The correct option is B $4.71A^o$

IE of H atom = 13.6 eV

Incident energy = 1.5 $\times$ IE = 1.5 $\times$ 13.6 eV

KE of e${}^{-}$ ejected out = 1.5 $\times$ 13.6 - 13.6 = 0.5 $\times$ 13.6

E${}_k$ = 0.5 $\times$ 13.6 eV = 6.8 $\times$ 1.6 $\times$ 10${}^{-19}$ J

$\lambda$ = $\frac{h}{\sqrt{2Em}}$ = $\frac{6.62\times {10}^{-34}Js}{2\times 6.8\times 9.1\times {10}^{-31}kg\times 1.6\times {10}^{-19}{)}^{1/2}}$

= $\frac{6.62\times {10}^{-9}}{14.07}$

$\lambda$ = $4.71A^0$