Wave Length and Frequency

Question

Radio astronomers use radio frequency waves to identify the elements in distant stars. One of the lines that is studied is designated the 166α166α line. This spectral line refers to the transition in hydrogen from 𝑛i=167ni=167 to 𝑛f=166.nf=166. Calculate the wavelength 𝜆λ and frequency 𝑓f of the electromagnetic radiation that is emitted for the 166α166α transition.

λ= m

𝑓= Hz

Answer 1

Using Bohr Model E_nm = E₁(1/m² - 1/n²) where n is the higher energy level and E₁ is the ground state energy of the Hydrogen atom: 13.6 eV or 2.18x10^-18Joules. I recommend the Joules for further calculation.

This transition energy is (2.18 x 10^-18 J) (1/166² - 1/167²)

Frequency, f = (E in Joules) / h (h is Plancks Constant in J-s)

and wavelength, λ = c/f where c is the speed of light, 3.00 x 10⁸ m/s

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