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

ID: 1376479 • Letter: T

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

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

E = hc/(lambda)

so to have longest wavelength, E must be smallest

E = 3.401 - 1.512 = 1.889 eV

E = hc/(lambda)

lambda = 6.63*10^-34 * 3*10^8/(1.6*10^-19 * 1.889) = 6.58*10^-7 m = 658 nm

Now,

E = hc/(lambda)

so to have shortest wavelength, E must be largest

E = 3.401 - .378 = 3.023 eV

E = hc/(lambda)

lambda = 6.63*10^-34 * 3*10^8/(1.6*10^-19 * 3.023) = 4.11*10^-7 m = 411 nm

Shortest possible wavelength will be where energy chnage is largest, so 411nm is answer