The wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from the $n = 2$ state to the ground state is closest to which of the following values? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = \right.$ $6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )
A) $243 \mathrm {~nm}$
B) $411 \mathrm {~nm}$
C) $203 \mathrm {~nm}$
D) $389 \mathrm {~nm}$
E) $122 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The energy difference between the $n = 2$ and $n = 1$ states in a hydrogen atom is 10.2 eV. Using the formula $E = \frac{hc}{\lambda}$, we find $\lambda = \frac{hc}{E}$. Substituting the given values, $\lambda \approx 122 \mathrm{~nm}$.

The Wavelength of the Emitted Photon If an Electron in the Hydrogen