What is the wavelength of the line in the Paschen series of hydrogen that is comprised of transitions from the n = 4 to the n = 3 levels? (R = 1.097 x 10⁷ m^-1 and 1 nm = 10^-9 m) A)1 282 nm B)1 875 nm C)1 923 nm D)2 251 nm

Question

Quizplus · Accepted Answer

The wavelength of a line in the Paschen series of hydrogen can be calculated using the formula:

1/λ = R(1/n1^2 - 1/n2^2)

where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels of the electron in the hydrogen atom.

For the transition from n=4 to n=3, we have:

1/λ = R(1/4^2 - 1/3^2)

Using the value of the Rydberg constant given in the question, and converting 1 nm to meters, we get:

1/λ = (1.097 x 10^7 m^-1) x (1/16 - 1/9)

1/λ = 2.363 x 10^6 m^-1

λ = 1/2.363 x 10^6 m^-1 = 1.875 x 10^-7 m = 1875 nm

Therefore, the correct answer is choice B) 1 875 nm.

What Is the Wavelength of the Line in the Paschen