Question

Spectral Absorption and Emission

Consider a hydrogen atom with an electron initially in the n = 4 state.

a) List the 3 different wavelengths that could be observed in the emission spectrum for this atom given the electron begins in level n = 4.

b) What is the longest wavelength photon that could potentially be absorbed by the electron in the level n = 4?

c) How much energy would be required to ionize this atom?

d) What is the maximum wavelength of the photon necessary to produce ionization?

Answer 1

(a)

When electron goes from n = 4 to n = 3,

1 / = R*z^2 * (1 / n1^2 - n2^2)

1 / = R*(1 / 3^2 - 1 / 4^2)

(1 / R = 912 A^o)

1 = 1.87 um

for n = 4 to n = 2

1 / = R*(1 / 2^2 - 1 / 4^2)

2 = 0.486 um

for n = 4 to n = 1

1 / = R*(1 - 1 / 4^2)

3 = 0.0972 um

(b)

longest wavelength,

= 1.87 um

(c)

Energy for ionization (from n = 4 to n = ),

E = -13.6 * (1 / - 1 / 4^2)

E = 0.85 eV

(d)

E = 0.85 eV = 1.36*10^(-19) J

= hc / E

= 2*10^(-25) / 1.36*10^(-19)

max = 1.47 um