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 $K_{\alpha }-line$
$\frac{1}{{\lambda }_{\alpha }}=R(Z-1{)}^2(\frac{1}{1^2}-\frac{1}{2^2})$
$=R(Z-1{)}^2\times \frac{3}{4}$
$R(Z-1{)}^2=\frac{4}{3{\lambda }_{\alpha }}$
Ionisation energy is given by
$E=Rhc(Z-1{)}^2(\frac{1}{1^2}-\frac{1}{\infty })$
$=hc\frac{4}{3{\lambda }_{\alpha }}$
$=\frac{6.6\times 10^{-34}\times 3\times 10^8\times 4}{3\times 1.54\times 10^{-10}}$
$=1.7\times 10^{-15}J$