Question

Radio astronomers use radio frequency waves to identify the elements in distant stars. One of the lines that is studied is designated the 166α line. This spectral line refers to the transition in hydrogen from ni = 167 to nf = 166. Calculate the wavelength λ and frequency f of the electromagnetic radiation that is emitted for the 166α transition.

Answer 1

1)

Here photon will be emitted

1/wavelength = R* (1/nf^2 - 1/ni^2)

R is Rydberg constant. R = 1.097*10^7

1/wavelength = R* (1/nf^2 - 1/ni^2)

1/wavelength = 1.097*10^7* (1/166^2 - 1/167^2)

wavelength = 0.2104 m

Answer: 0.2104 m

2)

we have:

wavelength = 0.2104 m

we have below equation to be used:

frequency = speed of light/wavelength

=(3.0*10^8 m/s)/(0.2104 m)

= 1.43*10^9 Hz

Answer: 1.43*10^9 Hz