Question

As the quantum number increases, the difference of energy between consecutive energy levels

• A. decreases
• B. increases
• C. sometimes increases sometimes decreases
• D. remains the same

Answer 1

Answer: (A)

Total energy in nth Bohr's orbit
$E_n=-\frac{13.6}{n^2}eV$
where n is the principal quantum number.
$E_2-E_1=-13.6(\frac{1}{(1{)}^2}-\frac{1}{(2{)}^2})$
$=-13.6(\frac{1}{4}-\frac{1}{1})=\frac{13.6\times 3}{4}$
$=0.75\times 13.6eV$
$E_3-E_2=-13.6(\frac{1}{3^2}-\frac{1}{2^2})$
$=-13.6(\frac{1}{9}-\frac{1}{4})$
$=13.6\times \frac{5}{36}$
$=0.14\times 13.6eV$
Therefore, the energy difference between consecutive energy levels decreases with increase in quantum number.