The Balmer series for the hydrogen atom corresponds to electronic transitions th

Question

The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n = 2 as shown in the figure below. Consider the photon of longest wavelength corresponding to a transition shown in the figure.

(a) Determine its energy.
___eV

(b) Determine its wavelength.
___nm

Consider the spectral line of shortest wavelength corresponding to a transition shown in the figure.

(c) Find its photon energy.
___eV

(d) Find its wavelength.
___nm

(e) What is the shortest possible wavelength in the Balmer series?
___nm

Explanation / Answer

a. The energy of the photon will be E = -1.512 - (-3.401) = 1.889 eV

b. The wavelength will be = hc/E = 6.626 x 10-34 x 3 x 108/ (1.889 x 1.6 x 10-19) = 658 nm

c. The photon energy will be E = -0.378 - (-3.401) = 3.023 eV

d. The wavelength will be = hc/E = 6.626 x 10-34 x 3 x 108/ (3.023 x 1.6 x 10-19) = 411nm

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