Calculate the wavenumber of a photon emitted | vedclass

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Question

(A) The formula for the wavenumber $(\bar{
u})$ is given by the Rydberg equation: $\bar{
u} = R_{H} \left[ \frac{1}{n_f^2} - \frac{1}{n_i^2} ight]

Vedclass · Accepted Answer

$15232.9$

Vedclass · Answer

(A) The formula for the wavenumber $(\bar{
u})$ is given by the Rydberg equation: $\bar{
u} = R_{H} \left[ \frac{1}{n_f^2} - \frac{1}{n_i^2} ight] \ cm^{-1}$ Given $n_f = 2$,$n_i = 3$,and $R_{H} = 109677 \ cm^{-1}$. Substituting the values: $\bar{
u} = 109677 \left[ \frac{1}{2^2} - \frac{1}{3^2} ight] \ cm^{-1}$ $= 109677 \left[ \frac{1}{4} - \frac{1}{9} ight] \ cm^{-1}$ $= 109677 \left[ \frac{9-4}{36} ight] \ cm^{-1}$ $= 109677 \left[ \frac{5}{36} ight] \ cm^{-1}$ $= 15232.9 \ cm^{-1}$

Calculate the wavenumber of a photon emitted during the transition from the orbit of $n=3$ to $n=2$ in a hydrogen atom. $(R_{H} = 109677 \ cm^{-1})$ (in $cm^{-1}$)

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