The Iongest wavelength photon that can be emitted by a hydrogen atom, for which the final state is $n = 9$, is closest to which one of the following values? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right.$, $\left. h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$
A) $28,000 \mathrm {~nm}$
B) $7400 \mathrm {~nm}$
C) $16,000 \mathrm {~nm}$
D) $22,000 \mathrm {~nm}$
E) $39,000 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The longest wavelength corresponds to the smallest energy transition, which is from $n = 10$ to $n = 9$. Using the Rydberg formula for hydrogen, calculate the energy difference and convert it to wavelength. The longest wavelength is approximately 39,000 nm.

The Iongest Wavelength Photon That Can Be Emitted by a Hydrogen