Question

An astrophysicist working at an observatory is interested in finding clouds of hydrogen in the galaxy. Usually hydrogen is detected by looking for the Balmer series of spectral lines in the visible spectrum. Unfortunately, the instrument that detects hydrogen emission spectra at this particular observatory is not working very well and only detects spectra in the infrared region of electromagnetic radiation. Therefore the astrophysicist decides to check for hydrogen by looking at the Paschen series, which produces spectral lines in the infrared part of the spectrum. The Paschen series describes the wavelengths of light emitted by the decay of electrons from higher orbits to the n=3 level. What wavelength should the astrophysicist look for to detect a transition of an electron from the n=7 to the n=3 level?

Answer 1

Answer:

1005 nm

Explanation:

This problem requires the use of Rydberg´s equation to calculate the wavelength:

1/λ = Rh x ( 1/n₁² - 1/n₂² ) where λ is the wavelength,

                                                  Rh = Rydberg´s constant, 1097 x 10⁷ / m

                                                   n₁ and n₂ are the energy levels (n₁ < n₂)

                                                   (n₁ = 3 , n₂ = 7 for this question)

All the data needed is given, so lets calculate the wavelength.

1/λ = 1.097 x 10⁷ / m x ( 1/3²  - 1/7² ) =  1.097 X 10⁷ /m x 9.07 x 10⁻²

     = 9.95 x 10⁵ / m

λ  = 1 / 9.95 x 10⁵ / m  = 1.05 x 10⁻⁶ m

It is customary to express the wavelength is nanometers, so

1.01 x 10⁻⁶ m x 1 x 10⁹ nm/ m = 1005 nm