Question

The wavelength of $K_{\alpha}-$ line in copper is $1.54 \, \, \mathring {A}. $ The ionisation energy of K-electron in copper in joule is

• A. $11.2 \times 10^{-17}$
• B. $12.9 \times 10^{-16}$
• C. $1.7 \times 10^{-15}$
• D. $10 \times 10^{-16}$

Answer 1

Answer: (C)

For $K_{\alpha}-line$
$\frac {1}{\lambda_{\alpha}}=R(Z-1)^2\bigg (\frac {1}{1^2}- \frac {1}{2^2}\bigg ) $
$ =R(Z-1)^2 \times \frac {3}{4} $
$ R(Z-1)^2 =\frac {4}{3 \lambda_{\alpha}} $
Ionisation energy is given by
$ E=Rhc(Z-1)^2\bigg (\frac {1}{1^2}- \frac {1}{\infty}\bigg ) $
$ =hc \frac {4}{3 \lambda_{\alpha}}$
$ =\frac {6.6 \times 10^{-34}\times3\times10^8\times4 }{3\times1.54\times10^{-10}}$
$=1.7 \times 10^{-15}J$