Ncert Exercises & Solutions

2.34 Calculate the energy required for the process

${He}^{+}_{(g)} \overset{}{\to} {He}^{2 +}_{(g)} + e^{-}$

The ionization energy for the H atom in the ground state is 2.18 × $10^{- 18}$ J ${atom}^{- 1}$

Energy associated with hydrogen-like species is given by,
$E_{n} = - 2.18 x 10^{- 18} (\frac{Z^{2}}{n^{2}}) J$
For ground state of hydrogen atom,

$∆ E = E_{\infty} - E_{1}$
$= 0 - [- 2.18 x 10^{- 18} \{\frac{{(1)}^{2}}{{(1)}^{2}}\}] J$
$∆ E = 2.18 x 10^{- 18} J$

For the given process,

${He}^{+}_{(g)} \overset{}{\to} {He}^{2 +}_{(g)} + e^{-}$

An electron is removed from n = 1 to n = ∞.

$∆ E = E_{\infty} - E_{1}$
$= 0 - [- 2.18 x 10^{- 18} \{\frac{{(2)}^{2}}{{(1)}^{2}}\}] J$
$∆ E = 8.72 x 10^{- 18} J$

$∴$ The energy required for the process is 8.72 x $10^{- 18}$ J.