Question

An electron and a proton are separated by a large distance and the electron approaches the proton with a kinetic energy of 4.11 eV. If the electron is captured by the proton to form a hydrogen atom in the ground state. the wavelength of photon given off is $\alpha \times {10}^2{A}^o$. What is the value of $\alpha$?

• A. 2
• B. 6.7
• C. 6.29
• D. None of these

Answer 1

The correct option is D None of these

Kinetic energy= Energy of photon

$\therefore 4.11\times 1.6\times {10}^{-19}=\frac{hc}{\lambda }=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{\lambda }$

$\therefore \lambda =\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{4.11\times 1.6\times {10}^{-19}}$

$\therefore \lambda =3.0228\times {10}^{-7}m$

$\therefore \lambda =\mathrm{3.022.8}\times {10}^{-10}m$

$\therefore \lambda =30.22\times {10}^2\stackrel{o}{A}$

Therefore, $\alpha =30.22$

Hence,option D is correct.