### Solutions to Example problems #5, 6 and 7

Return to discussion of E = hν

**Problem #5:** What is the energy of a photon of green light with a frequency of 5.76 x 10^{14} s¯^{1}.

Solution:

x = (6.626 x 10¯^{34} J s) (5.76 x 10^{14} s¯^{1})
x = 3.82 x 10¯^{19} J

Comment: all frequencies of visible light will have an energy in the 10¯^{19} J range of values. If you wish to, you may calculate this for yourself. The wavelength range of visible light is taken to be from 400 nm to 700 nm. This translates (more-or-less) to a range from 5 x 10¯^{19} J down to 3 x 10¯^{19} J.

**Problem #6:** A particular x-ray has a wavelength of 1.2 Å. Calculate the energy of one mole of photons with this wavelength.

Solution:

1.2 Å x (10¯^{8} cm / 1 Å) = 1.2 x 10¯^{8} cm
(x) (1.2 x 10¯^{8} cm) = (6.626 x 10¯^{34} J s) (3.00 x 10^{10} cm s¯^{1})

Comment: I used Eλ = hc. Note also that I used 3.00 x 10^{10} cm s¯^{1} for the speed of light. I did this because the 1.2 Ångstrom value for the wavelength converts very easily into cm. There was no need to take the wavelength to meters.

x = 1.66 x 10¯^{15} J

This is the energy for one photon. To get energy per mole, multiply the above value by Avogadro's Number:

(1.66 x 10¯^{15} J) (6.022 x 10^{23} mol¯^{1}) = 9.98 x 10^{8} J mol¯^{1}
This value is usually reported in kJ per mole: 9.98 x 10^{5} kJ mol¯^{1}

**Problem #7:** When excited, some atoms produce an emssion with a frequency of 7.25 x 10^{12} Hz.

(a) calculate the energy, in Joules, for one photon with this frequency.

(b) calculate the energy, in kJ/mol.

(c) Is this light visible? Why or why not?

Comments on the solution:

(a) use E = hν
(b) use Avogadro's number as well as the answer from (a). Make sure to convert from the J value (which is what you'll calculate) to the kJ value.

(c) Calculate the wavelength using λν = c. What you need to do is compare the wavelength you calculate to the commonly accepted range of visible wavelengths, which is 400 nm to 700 nm. The wavelength you calculate will probably be in meters, so you will need to convert it to nm, then compare.

Return to discussion of E = hν