The shortest wavelength of a photon that can be emitted by a hydrogen atom,for which the initial state is n = 3,is closest to:
A)820 nm
B)850 nm
C)880 nm
D)910 nm
E)940 nm

Question

Quizplus · Accepted Answer

The shortest wavelength corresponds to the largest energy difference, which occurs when the electron transitions from n = 3 to n = 1. The energy difference between these levels is given by:E = -13.6 eV * (1/1^2 - 1/3^2) = -12.1 eVThe wavelength of a photon with this energy is given by:λ = hc/E = (6.626 x 10^-34 J s) * (3 x 10^8 m/s) / (-12.1 eV * 1.602 x 10^-19 J/eV) = 820 nmTherefore, the shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is n = 3, is closest to 820 nm.

The Shortest Wavelength of a Photon That Can Be Emitted