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Question

(A) The frequency $
u$ of the emitted radiation is given by the Rydberg formula: $
u = c R Z^2 [1/(n-1)^2 - 1/n^2]$.Simplifying the expression insid

Vedclass · Accepted Answer

$1/n^3$

Vedclass · Answer

(A) The frequency $
u$ of the emitted radiation is given by the Rydberg formula: $
u = c R Z^2 [1/(n-1)^2 - 1/n^2]$.Simplifying the expression inside the brackets: $[n^2 - (n-1)^2] / [n^2(n-1)^2] = (n^2 - (n^2 - 2n + 1)) / [n^2(n-1)^2] = (2n - 1) / [n^2(n-1)^2]$.Since $n >> 1$,we can approximate $(2n - 1) \approx 2n$ and $(n-1) \approx n$.Substituting these approximations: $
u \approx c R Z^2 [2n / (n^2 \cdot n^2)] = c R Z^2 [2n / n^4] = 2 c R Z^2 / n^3$.Therefore,the frequency $
u$ is proportional to $1/n^3$.

In a hydrogen-like atom,an electron makes a transition from an energy level with quantum number $n$ to another with quantum number $(n - 1)$. If $n >> 1$,the frequency of radiation emitted is proportional to:

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