Solar Radiation Heat Balance And Temperature

Concept: The energy of a photon is given by the Planck–Einstein relation:

E%20%3D%20%5Cfrac%7Bhc%7D%7B%5Clambda%7D

where:

$E$ = Energy of the photon
$h$ = Planck’s constant $%3D%206.6%20%5Ctimes%2010%5E%7B-34%7D%5C%20%5Ctext%7BJs%7D$
$c$ = Speed of light $%3D%203%20%5Ctimes%2010%5E8%5C%20%5Ctext%7Bm%2Fs%7D$
$%5Clambda$ = Wavelength of the photon

Before substituting, convert the wavelength from nanometers to meters:

500%5C%20%5Ctext%7Bnm%7D%20%3D%20500%20%5Ctimes%2010%5E%7B-9%7D%5C%20%5Ctext%7Bm%7D%20%3D%205%20%5Ctimes%2010%5E%7B-7%7D%5C%20%5Ctext%7Bm%7D

Step 1: Substitute the values into the photon energy formula.

E%20%3D%20%5Cfrac%7B(6.6%20%5Ctimes%2010%5E%7B-34%7D)(3%20%5Ctimes%2010%5E8)%7D%7B5%20%5Ctimes%2010%5E%7B-7%7D%7D

Step 2: Simplify the numerator.

6.6%20%5Ctimes%203%20%3D%2019.8

E%20%3D%20%5Cfrac%7B19.8%20%5Ctimes%2010%5E%7B-26%7D%7D%7B5%20%5Ctimes%2010%5E%7B-7%7D%7D

Step 3: Divide the coefficients and adjust powers of ten.

E%20%3D%203.96%20%5Ctimes%2010%5E%7B-19%7D%5C%20%5Ctext%7BJ%7D

Thus, the energy of the photon is:

E%20%3D%203.96%20%5Ctimes%2010%5E%7B-19%7D%5C%20%5Ctext%7BJ%7D

Chapter Questions
1 MCQs