Question

The wavelength of electromagnetic radiation required to eject the electron from the first orbit to infinity is given by

• A. 25.28 Å
• B. $\lambda =252.8$Å
• C. $0.2528$Å
• D. $\lambda =2.528$Å

Answer 1

The correct option is A 25.28 Å

Energy required to eject the electron from the first Bohr orbit $E_1$ to infinity $(E_{\infty }=0)$ is
$hv=E_{\infty }-E_1=0-(-489.6eV)=489.6eV$
or $\frac{hl}{\lambda }=489.6\times 1.6\times {10}^{-19}J$

$\lambda =\frac{hc}{489.6\times 1.6\times {10}^{19}}=\frac{(6.6\times {10}^{34})\times (3\times {10}^8)}{489.6\times 1.6\times {10}^{19}}$

$\lambda =25.28$ Å