Question

The energy levels of a hypothetical one electron atom are shown in the figure above. Find the wave number of the photon emitted for the transition $n=3$ to $n=1$.

• A. $2.23\times {10}^7{m}^{-1}$
• B. $1.007\times {10}^7{m}^{-1}$
• C. $3.005\times {10}^6{m}^{-1}$
• D. $0.432\times {10}^6{m}^{-1}$

Answer 1

The correct option is B $1.007\times {10}^7{m}^{-1}$

Wavenumber $\left(\overline{\nu }\right)$ is inverse of wavelength.
Therefore, $\overline{\nu }=\frac{E}{hc}$
Energy released is: $15.6-3.08=12.52eV$
Therefore, $\overline{\nu }=\frac{12.52\times 1.602\times {10}^{-19}}{(6.625\times {10}^{-34})(3\times {10}^8)}\approx 1.007\times {10}^7{m}^{-1}$