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Question: Answered & Verified by Expert
The frequency $v$ of the radiation emitted by an atom when an electron jumps from one orbit to another is given by $=\mathrm{k} \delta \mathrm{E}$, where $\mathrm{k}$ is a constant and $\delta \mathrm{E}$ is the change in energy level due to the transition. Then dimension of $\mathrm{k}$ is
PhysicsUnits and DimensionsJEE Main
Options:
  • A $\mathrm{ML}^{2} \mathrm{~T}^{-2}$
  • B the same dimension of angular momentum
  • C $\mathrm{ML}^{2} \mathrm{~T}^{-1}$
  • D $\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}$
Solution:
1237 Upvotes Verified Answer
The correct answer is: $\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}$
Hint:
$v=k \delta E$
$[k]=\left[\frac{v}{\delta E}\right]=\frac{\left[T^{-1}\right]}{\left[M L^{2} T^{-2}\right]}$
$[k]=\left[M^{-} L^{-2} T^{1}\right]$

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