In the following, use Bohr’s model to describe the emission of a photon of wavel

ID: 484503 • Letter: I

Question

In the following, use Bohr’s model to describe the emission of a photon of wavelength 4,048 nm from an excited hydrogen atom.

a) What is the energy of this photo in Joules? Rydbergs? Electronvolts? What part of the electromagnetic spectrum is this light in?

b) Assuming that the emission came from a transition between consecutive energy levels, what was the initial energy level of this emission (ni)?

c) What is the distance of the initial level from the nucleus (ri) in Bohr radii and in meters?

d) How much closer to the nucleus is the electron in its final energy excited state than the initial state? What percent closer?

a) energy of photon (E) = hc/

(h = planck's constant , c = speed of light. = wavelength)

E = (6.63 x10-34 x 3.0x108 ) / ( 4048 x10-9 m )

E = 4.913 x10-20 joules

1 joule = 6.242 x1018 ev

E = 4.913 x10-20 joules x 6.242 x1018 ev = 30.66 x10-2 ev = 2.2537 x10-2 redberg

ultravoilet electromagnetic wave

b) E = Eo (1/n12 - 1/n22) ....(Eo = 13.6 ev )

E = 30.66 x10-2 ev = 13.6 ( 1/n12 - 1/n1+12 ) ......(for consecutive transition)

0.0225 = (1/n12 - 1/n1+12 )

n1 = 4 and n2 = 5

c) radii (rn) = 52.9 n2 / Z

rn = 52.9 x 42 / 1 ....(hydrogen Z = 1)

rn = 846.4 pm = 8.464x10-10 m = 15.909 bohr redii

d) rn = 52.9 x 52 = 1322.5 pm = 1.3225 x10-9 m ....(distance from nucleus )

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