Question

The ionization energy of $10$ times ionized sodium atom is

• A. $ \frac{13.6}{11}eV $
• B. $ \frac{13.6}{{{(11)}^{2}}}eV $
• C. $ 13.6\times {{(11)}^{2}}eV $
• D. $ 13.6\,eV $

Answer 1

Answer: (C)

The Bohr model of hydrogen atom can be extended to hydrogen like atoms. Energy of such an atom is given by
$E_{n}=-13.6 \frac{Z^{2}}{n^{2}}$
Here, $Z=11$ for $N a$ atom; $10$ electrons are removed already, so it is $10$ limes ionised.
For the last electron to be removed, $n=1$
$ \therefore $ $E_{n}=\frac{13.6(11)^{2}}{(1)^{2}} \,e V$
or $E_{n}=-13.6 \times(11)^{2}\, e V$