Question

Using arbitrary energy units we can calculate that $864$ $\text{arbitrary units (a.u.)}$ are required to transfer an electron in hydrogen atom from the most stable Bohr's orbit to the largest distance from the nucleus.
$n=\infty ;E=0$
$n=1;E=-864$ $\text{Arbitrary units}$
The energy required to transfer the electron from third Bohr's orbit to the orbit $n=\infty$ will be :

• A. $96\text{Arbitrary units}$
• B. $192\text{Arbitrary units}$
• C. $288\text{Arbitrary units}$
• D. $384\text{Arbitrary units}$

Answer 1

The correct option is A $96\text{Arbitrary units}$

The energy of first Bohr's orbit of $H-\text{atom}=-\frac{2{\pi }^{2}m{e}^4}{h^2}=-864$
The energy of third Bohr's orbit of $H-\text{atom}=-\frac{2{\pi }^{2}m{e}^4}{h^2}\times \frac{1}{3^2}=-864\times \frac{1}{9}=-96\text{Arbitrary units}$
$\text{Energy required to separate the electron}=E_{\infty }-E_n=0-(-96)=96\text{Arbitrary units}$