Question

For a hydrogen atom, calculate the wavelength of an emitted photon in the Lyman series that results from the transition n = 3 to n = 1. The Rydberg constant is 2.18 x 10^-18 J.

Answer 1

Apply Rydberg Formula

E = R*(1/nf^2 – 1/ni ^2)

R = -2.178*10^-18 J

Nf = final stage/level

Ni = initial stage/level

E = Energy per unit (i.e. J/photon)

nf = 1; ni = 3

E = (-2.178*10^-18)*(1/1^2 – 1/3 ^2)

E = 1.936*10^-18

For the wavelength:

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = wavelength in meters

WL = (6.626*10^-34)(3*10^8)/(1.936*10^-18)

WL = 1.0267*10^-7 m

to nanometers:

WL = (1.0267*10^-7)(10^9) = 102.67 nm