Question

The ratio of the difference in energy between the first and second Bohr orbit to that between second and third Bohr in H-atom is:

• A. $4/9$
• B. $1/3$
• C. $27/5$
• D. $1/2$

Answer 1

Answer: (C)

$27/5$

Let us consider the problem:

$E_1-E_2=1312\times Z^2\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=1312\times Z^2\left(\frac{3}{4}\right)$

$E_2-E_3=1312\times Z^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$

Implies that

$=1312\times Z^2\left(\frac{5}{36}\right)$

From these equation:

$\frac{E_1-E_2}{E_2-E_3}=\frac{3\times 36}{4\times 5}=\frac{27}{5}$.