Question

An electron, in a hydrogen atom, in its ground state absorbs $1.5$ times as much energy as the minimum required for its escape (i.e., $13.6eV$) from the atom. Calculate the value of $\lambda$ for the emitted electron.

• A. $4.69\mathring{A}$.
• B. $3.9\mathring{A}$.
• C. $7.9\mathring{A}$.
• D. $46.9\mathring{A}$.

Answer 1

The correct option is A $4.69\mathring{A}$.

Energy observed $=13.6\times 1.5=20.4eV$

Energy required$=13.6eV$

$\therefore$ Excess energy$=6.8eV=6.8\times 1.6\times {10}^{-19}J=Ke$

$\lambda =\frac{h}{mc}$

$\lambda =\frac{h}{\sqrt{2mk}}=\frac{6.626\times {10}^{-34}}{\sqrt{2\times 9.1\times {10}^{-31}\times 6.8\times 1.6\times {10}^{-19}}}\lambda =4.7\mathring{A}$