Q. The ratio of the difference in energy between the first and the second Bohr orbit to that between the second and the third Bohr orbit is
A) $\frac{1}{2}$
B) $\frac{1}{3}$
C) $\frac{4}{9}$
D) $\frac{27}{5}$
Explanation
(d)
$E_{1} - E_{2} = 1312 \times Z^{2}\left\lbrack \frac{1}{1^{2}} - \frac{1}{2^{2}} \right\rbrack$
$E_{1} - E_{2} = 1312 \times Z^{2}\left\lbrack \frac{3}{4} \right\rbrack\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
$E_{2} - E_{3} = 1312 \times Z^{2}\left\lbrack \frac{1}{2^{2}} - \frac{1}{3^{2}} \right\rbrack$
$E_{2} - E_{3} = 1312 \times Z^{2}\left\lbrack \frac{5}{36} \right\rbrack\ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
From Eqs. (i) and (ii)
$\frac{E_{1} - E_{2}}{E_{2} - E_{3}} = \frac{3 \times 36}{4 \times 5} = \frac{27}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.