Question

Find the wavelength of the third line in the Lyman series, and identify the type of EM radiation.

a) 102.6 nm, Ultraviolet
b) 97.3 nm, Infrared
c) 121.6 nm, Ultraviolet
d) 145.5 nm, X-ray

Answer 1

The wavelength of the third line in the Lyman series is 121.6 nm, which corresponds to Ultraviolet radiation.

Step-by-step explanation:

The Lyman series is a series of spectral lines in the hydrogen atom spectrum. The wavelength of the third line in the Lyman series can be found using the formula:

1/λ = R(1/1^2 - 1/n^2)

where λ is the wavelength, R is the Rydberg constant, and n is the energy level of the electron.

Substituting the values, we find:

1/λ = R(1 - 1/3^2)

Simplifying the equation gives us:

1/λ = 8R/9

Since the third line in the Lyman series corresponds to the transition from the n=3 to n=2 energy levels, we can substitute n=2 into the equation:

1/λ = 8R/9

1/λ = 8 × (1.097 × 10^7 m^-1)/9

Solving for λ, we get:

λ = 121.6 nm

The type of electromagnetic radiation for a wavelength of 121.6 nm is Ultraviolet.