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# The ratio of the difference in energy between the first and second Bohr orbit to that between the second and the third Bohr orbit is

$\begin{array}{1 1} (a)\;\large\frac{1}{2} \\ (b)\;\large\frac{1}{3} \\ (c)\;\large\frac{4}{9} \\(d)\;\large\frac{27}{5} \end{array}$

$E_1-E_2=1312 \times Z^2 \bigg(\large\frac{1}{1^2}-\frac{1}{2^2}\bigg)$$=1312 \times Z^2\bigg(\large\frac{3}{4}\bigg)$
$E_2-E_3=1312 \times Z^2 \bigg(\large\frac{1}{2^2}-\frac{1}{3^2}\bigg)$
$\qquad= 1312 \times Z^2\bigg(\large\frac{5}{36}\bigg)$
$\large\frac{E_1-E_2}{E_2-E_3}=\frac{3 \times 36}{4 \times 5}=\frac{27}{5}$