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(A) The frequency $f$ of the emitted radiation is given by $f = c / \lambda = cR [1/(n-1)^2 - 1/n^2]$.Simplifying the expression: $f = Rc [n^2 - (n-1)

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$\frac{1}{n^3}$

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(A) The frequency $f$ of the emitted radiation is given by $f = c / \lambda = cR [1/(n-1)^2 - 1/n^2]$.Simplifying the expression: $f = Rc [n^2 - (n-1)^2] / [n^2(n-1)^2]$.$f = Rc [n^2 - (n^2 - 2n + 1)] / [n^2(n-1)^2] = Rc (2n - 1) / [n^2(n-1)^2]$.Since $n >> 1$,we can approximate $(n-1) \approx n$ and $(2n - 1) \approx 2n$.Substituting these approximations: $f \approx Rc (2n) / [n^2(n^2)] = 2Rc / n^3$.Therefore,$f \propto 1/n^3$.

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

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