Question

An electron in hydrogen atom in its ground state absorbs energy equal to the ionisation energy of ${Li}^{2+}$. What will be the wavelength of emitted radiation, when electron returns to normal state?

• A. $3.32\mathring{A}$
• B. $2.32nm$
• C. $1.14\mathring{A}$
• D. $3.33pm$

Answer 1

The correct option is C $1.14\mathring{A}$

Ground state energy of hydrogen atom:

$E=-2.18\times {10}^{-18}J$

Ionisation energy $=+\frac{Z^2}{n^2}\times 2.18\times {10}^{-18}J$

$=\frac{9}{1^2}\times 2.18\times {10}^{-18}J$

Total energy after absorption $=-2.18\times {10}^{-18}+9\times 2.18\times {10}^{-18}$

$=8\times 2.18\times {10}^{-18}J$

$E=\frac{hc}{\lambda }$

$\lambda =\frac{hc}{E}=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{8\times 2.18\times {10}^{-18}}$

$=1.139\times {10}^{-8}cm=1.14\times {10}^{-10}m=1.14\mathring{A}$.

Hence, the correct option is $\text{C}$