Question

Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model ?

• A. $0.65eV$
• B. $1.9eV$
• C. $11.1eV$
• D. $13.6eV$

Answer 1

The correct option is C

$11.1eV$

The energy of n^th orbit of hydrogen atom is given by $E_n=\frac{-13.6}{n^2}eV$

For 1^st energy orbit, $n=1\Rightarrow E_1=\frac{-13.6}{1^2}eV\Rightarrow E_1=-13.6eV$

For 2^nd energy orbit, $n=2\Rightarrow E_2=\frac{-13.6}{2^2}eV\Rightarrow E_2=-3.4eV$

For 3^rd energy orbit, $n=3\Rightarrow E_3=\frac{-13.6}{3^2}eV\Rightarrow E_3=-1.5eV$

For 4^th energy orbit, $n=4\Rightarrow E_4=\frac{-13.6}{4^2}eV\Rightarrow E_4=-0.85eV$

Changes in energy, $$\begin{gathered} E_3-E_2=-1.5-(-3.4)=1.9eV \\ {E}_4-E_3=-0.85-(-1.5)=0.65eV \end{gathered}$$

From the above we are not getting the energy as $11.1eV$, so not possible energy is $11.1eV$.

Hence option C is correct.