Question

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

• A. 4.21
• B. 4.71
• C. 3.52
• D. 3.711

Answer 1

The correct option is B 4.71

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
$\lambda$ = $\frac{h}{\sqrt{2Em}}$ = $\frac{6.62\times {10}^{-34}Js}{(2\times 6.8\times 9.1\times {10}^{-31}kg\times 1.6\times {10}^{-19}{)}^{1/2}}$
= $\frac{6.62\times {10}^{-9}}{14.07}$
$\lambda$ = $4.71A^o$