Question

In radio astronomy, hydrogen atoms are observed in which, for example, radiative transitions from n=109 to n=108 occur. What are the frequency and wavelength of the radiation emitted in this transition?

Answer 1

n = 109 to n = 108

using equation

E_n = 13.6 ( 1 - 1/n² ) eV

E₁₀₉ = 13.6 ( 1 - 1/109² )

= 13.59885532 eV

E_n = 13.6 ( 1 - 1/n² ) eV

E₁₀₈ = 13.6 ( 1 - 1/108² )

= 13.59883402 eV

dE = E₁₀₉ - E₁₀₈  

dE = 13.59885532 - 13.59883402

dE = 2.1296 X 10^-5 eV

or

dE = 2.1296 X 10^-5 X 1.6 X 10^-19

dE = 3.40736 X 10^-24 J

= hC/ dE

= 6.627 X 10^-34 X 3 X 10⁸ / 3.40736 X 10^-24

= 0.05834 m

or

= 5.834 cm

f = C /

f = 3 X 10⁸ / 0.05834

f = 5.142269455 X 10⁹ Hz

f = 5.142269455 GHz