The electron in a hydrogen atom, originally in level n = 8, undergoes a transition to a lower level by emitting a photon of wavelength 3745 nm. What is the final level of the electron? (c=3.00×108 m/s, h=6.63×10-34 J·s, RH=2.179×10-18 J)

n=5

Explanation:

Applying the Rydberg's equation

hc/l= RH[(1/nf^2)-(1/ni^2)

Let l= wavelength= 3745×10^-9m

h=6.63×10^-34 , c= 3.0×10^8, RH= 2.179×10^-18

Substitute into the Rydberg's equation and simplify

(6.63×10^-34×3×10^8)/3745×10^-9=2.179×10^-18(1/nf^2 -1/8^2)

0.024= 1/nf^2 -0.0156

0.024+0.0156= 1/nf^2

0.0396= 1/nf^2

nf^2= 25.3

Take square root of both sides

nf= 5.02=5