What is the wavelength of the line in the hydrogen spectrum that is comprised of transitions from the n = 5 to the n = 3 levels?
A) 1880 nm
B) 1290 nm
C) 2250 nm
D) 1920 nm

Question

Quizplus · Accepted Answer

To determine the wavelength of a hydrogen line, we use the formula:

1/λ = R(1/n1^2 - 1/n2^2)

where λ is the wavelength, R is the Rydberg constant (1.0974 x 10^7 m^-1), and n1 and n2 are the initial and final energy levels, respectively. Plugging in n1 = 5 and n2 = 3, we get:

1/λ = R(1/5^2 - 1/3^2) = 1.0974 x 10^7 m^-1 (1/25 - 1/9) = 1.0974 x 10^7 m^-1 (4/225) = 0.0000486 m^-1

Taking the reciprocal of this value gives us the wavelength:

λ = 1/0.0000486 m^-1 = 20,491 nm

Therefore, the correct answer is B, which is the closest option to 20,491 nm.

What Is the Wavelength of the Line in the Hydrogen