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

Part A)

The longest wavelength will result from a transition from n = 3 to n = 2

Using 1/ = R(1/nf2 - 1/ni2) we get

1/ = (1.097 X 107)(1/22 - 1/33)

= 6.563 X 10-7 m or 656.3 nm

Then, using E = hc/ we can find the energy

E = (6.63 X 10-34)(3 X 108)/(6.563 X 10-7) = 3.03 X 10-19 J

Since there are 1.062 X 10-19 J per eV, 3.03 X 10-19/1.602 X 10-19 = 1.89 eV

Part B)

Already solved in part A, needed that first

The longest wavelength will result from a transition from n = 3 to n = 2

Using 1/ = R(1/nf2 - 1/ni2) we get

1/ = (1.097 X 107)(1/22 - 1/33)

= 6.563 X 10-9 m or 656.3 nm

Part C)

The shortest wavelength shown will result from a transition from n = 6 to n = 2

Using 1/ = R(1/nf2 - 1/ni2) we get

1/ = (1.097 X 107)(1/22 - 1/62)

= 4.102 X 10-7 m or 410.2 nm

Then, using E = hc/ we can find the energy

E = (6.63 X 10-34)(3 X 108)/(4.102 X 10-7) = 4.849 X 10-19 J

Since there are 1.062 X 10-19 J per eV, 4.849 X 10-19/1.602 X 10-19 = 3.03 eV

Part D)

Already found in part C, needed it first

The shortest wavelength shown will result from a transition from n = 6 to n = 2

Using 1/ = R(1/nf2 - 1/ni2) we get

1/ = (1.097 X 107)(1/22 - 1/62)

= 4.102 X 10-7 m or 410.2 nm

Part E)

The shortest wavelength will result from a transition from n = infinity to n = 2

Using 1/ = R(1/nf2 - 1/ni2) we get

1/ = (1.097 X 107)(1/22 - 0)

= 3.646 X 10-7 m or 364.6 nm

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