A hydrogen atom emits light as it undergoes a transition fro

A hydrogen atom emits light as it undergoes a transition from the n = 4 state to the n = 2 state. Calculate the following.

(a) the energy
ev

(b) the wavelength
nm

(c) the frequency of the radiation
Hz

Solution

E = h c / lambda

= h c R_H [1/n_i² - 1/n_f²]

= 13.6 ev [1/2² - 1/4²] = 2.55 eV

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b) lambda = [ R_H [1/n_i² - 1/n_f²] ]^-1

= [ 1.097 * 10⁷[1/2² - 1/4²] ]^-1

= 486 nm

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c) f = c / lambda = (3 * 10⁸) / (486 nm)

= 6.17 * 10¹⁴ Hz