Question

Calculate the energy per photon and the energy per mole of photons for radiation of wavelength (a) 200 nm (ultraviolet), (b) 150 pm (X-ray), (c) 1.00 cm (microwave).

Answer 1

Answer: a. E =9.9*EXP(-19)J

1 mole E= 596178J

b. E= 1.32*EXP(-15)J, 1 mole E=795MegaJ

c. E= 1.98*EXP(-23)J

1 mole E = 11.9J

Explanation: The Energy of a photon E, the wavelength are related by

E= h*c/wavelength

h is the Planck's constant 6.6*EXP(-34)J.s

c is speed of light 3*EXP(8)m/s

h*c=1.98*EXP(-25)

Now let's solve

a. E = h*c/wavelength

= h*c/(200*EXP(-9)m

=9.9*EXP(-19)J

1 mole of a photon contian 6.022*EXP(23)photons by advogadro

Now to get the energy of 1 mole of the photon we have

9.9*EXP(-19)*6.023*EXP(23)

=596178J

b. E=h*c/150*EXP(-12)m

=1.32*EXP(-15)J

1 mole will have

1.32*EXP(-15)*6.022*EXP(23)J

=795*EXP(6)J

c. E= h*c/1*EXP(-2)m

=1.98*EXP(-23)J

1 mole of the photon will have

1.98*EXP(-23)J *6.022*EXP(23)

= 11.9J.

You will notice that the longer the wavelength of the photon the lesser the Energy it as.

NOTE: EXP represent 10^