The longest wavelength of a photon that can be emitted by a hydrogen atom,for which the final state is n = 9,is closest to:
A)39,000 nm
B)22,000 nm
C)7400 nm
D)16,000 nm
E)28,000 nm

Question

Quizplus · Accepted Answer

The longest wavelength involves the transition from n=10 to n=9. Using the Rydberg formula, we have:

1/λ = R(1/nf^2 - 1/ni^2)

where R is the Rydberg constant (1.097 x 10^7 m^-1), ni is the initial energy level (10 in this case), and nf is the final energy level (9). Plugging in the numbers, we get:

1/λ = 1.097 x 10^7 (1/81 - 1/100)

1/λ = 2.466 x 10^-5

λ = 40544.8 nm

Note that we rounded to four significant figures, which gives us answer A) 39,000 nm as the closest choice.

The Longest Wavelength of a Photon That Can Be Emitted