The Foundations of Chemistry

EXAMPLE 5-6 Energy of Light

A green line of wavelength 4.86 10
^7 m is observed in the emission spectrum of hydrogen.
Calculate the energy of one photon of this green light.

Plan
We know the wavelength of the light, and we calculate its frequency so that we can then calcu-
late the energy of each photon.

Solution

E4.09 10 
^19 J/photon

To gain a better appreciation of the amount of energy involved, let’s calculate the total energy,
in kilojoules, emitted by one mole of atoms. (Each atom emits one photon.)

4.09 10 
^19 2.46 102 kJ/mol

This calculation shows that when each atom in one mole of hydrogen atoms emits light of
wavelength 4.86 10
^7 m, the mole of atoms loses 246 kJ of energy as green light. (This
would be enough energy to operate a 100-watt light bulb for more than 40 minutes.)

You should now work Exercises 40 and 42.

6.02 1023 atoms



mol

1 kJ



1  103 J

J



atom

? k J

mol

(6.626 10 
^34 J s)(3.00 108 m/s)



(4.86 10 
^7 m)

hc





Figure 5-15 Atomic spectra in the visible region for some elements. Figure 5-14a shows
how such spectra are produced. (a) Emission spectra for some elements. (b) Absorption
spectrum for hydrogen. Compare the positions of these lines with those in the emission
spectrum for H in (a).

λ(Å) 4000 5000 6000 7000

(b)

H

4000 5000 6000 7000

Ne

Hg

H

(a)

λ(Å)