The Shortest Wavelength of a Photon That Can Be Emitted $n = 12$

Multiple Choice

The shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is $n = 12$ , is closest to which one of the following values? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right.$ , $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

A) $52 \mathrm {~nm}$
B) $72 \mathrm {~nm}$
C) $92 \mathrm {~nm}$
D) $82 \mathrm {~nm}$
E) $62 \mathrm {~nm}$