Question

If first and second frequencies in transition to ' $k$ ' orbital are related by the relation $v_{1}=k v_{2}$, then the first frequency in the transition to second orbital will not he equal to:

• A. $v_{1}\left(\frac{1}{k}-1\right)$
• B. $(1-k) v_{2}$
• C. $v_{2}-v_{1}$
• D. $k^{2} v_{2}$

Answer 1

Answer: (D)

We use
$v_{1} =\frac{E_{2}-E_{1}}{h} v_{2}=\frac{E_{3}-E_{1}}{h};$
$\Rightarrow v_{2}-v_{1} =\frac{E_{3}-E_{2}}{h}=v_{3}$
As $v_{1} =k v_{2} ; $
$\Rightarrow v_{3} =v_{2}(1-k)=\left(\frac{1}{k}-1\right) v_{1}$
Hence the only incorrect option is $v=k^{2} v_{2}$.