Question

A line in the Brackett series of hydrogen has a wavelength of 4052 nm. From what state did the electron originate?

Answer 1

Brackett series start i n = 4

so:

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)

E = (-2.178*10^-18)*(1/4^2 – 1/ni ^2)

we need E

from the wavelength:

E = h c / WL

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

E = (6.626*10^-34)(3*10^8)/(4052*10^-9) = 4.905*10^-20

then

E = (-2.178*10^-18)*(1/4^2 – 1/ni ^2)

4.905*10^-20 = (2.178*10^-18)*(1/4^2 – 1/ni ^2)

(4.905*10^-20)/(2.178*10^-18) = (1/4^2 – 1/ni ^2)

0.02252 =  (1/4^2 – 1/ni ^2)

0.02252 - 1/16 = -1/ni^2

-0.03998 = -1/ni^2

ni = sqrt(1/0.03998 )

ni = 5.00125