Question

For ionising an excited hydrogen atom, the energy required (in eV) will be

• A. a little less than 13.6
• B. 13.6
• C. more than 13.6
• D. 3.4 or less

Answer 1

Answer: (B)

There is only one electron in the hydrogen, atom. If this electron leaves the atom, the atom is ionised. The external energy required to ionise the atom is called its ionisation energy. Hydrogen atom normally stays in lowest energy state $ (n=1) $ , where its energy is $ {{E}_{1}}=\frac{Rhc}{{{1}^{2}}}=-Rhc $ On being ionized its energy becomes zero. Thus, ionization of hydrogen atom is $ =energy\text{ }after\text{ }ionisation-energy\text{ }before $ $ ionisation $ $ =0-(-Rhc)=Rhc $ $ =(1.097\times {{10}^{7}}{{m}^{-1}})(6.63\times {{10}^{-34}}J-s) $ $ (3\times {{10}^{8}}m{{s}^{-1}}) $ $ =21.8\times {{10}^{-19}}J $ $ =\frac{21.8\times {{10}^{-19}}}{1.6\times {{10}^{-19}}}=13.6\,eV $