EME 810
Solar Resource Assessment and Economics

Key Equations

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Mathematical Relationships for Light

This is another reference book page, which may become useful throughout the course, especialy when we tak about properties of light and light energy conversion. Feel fre to re-visit it later.

An electromagnetic wave can be characterized by its wavelength ( λ) and frequency ( ν). Mathematically, a simple relationship between these properties shows that

λ= c ν

where c= speed of light in a vacuum ( 3× 10 17 nm s )

All electromagnetic radiation is quantized and occurs in photons. The energy (E) depends on the frequency(f) of the electromagnetic radiation. This relationship is elegantly described by Planck's equation

E p =hν hc λ

where h=Planck's constant ( 4.1357× 10 15 eVs)

But we want a simple relation to convert between wavelength and energy (as eV). If we multiply Planck's constant times the speed of light (all in units of nm and eV), we get a simple equation like this:

E p = 1239.8 eVnm λ

or

λ= 1239.8 eVnm Ep

Even easier, just count to 5! For our approximation purposes (plenty good enough for the real spectrum), we can use these simpler equations as long as we remember our units and the decimal point:

E p = 1234.5 eVnm λ

or

λ= 1234.5 eVnm E p

Self Check using 1234.5/(argument)

Click on the question to reveal the correct answer.

1. The band gap of Silicon is 1.1 eV. What is that value in nanometers?

ANSWER: 1234.5 eVnm/1.1 eV is about 1100 nm. Putting 1100 back into the denominator yields 1.1 eV

2. The band gap of CdTe is about 1.5 eV. What is that in nanometers?

ANSWER: 1234.5 eVnm/1.5 eV is about 800 nm. Putting 800 back into the denominator still yields 1.5 eV

3. The visible spectrum is from 380-780 nm. What would that be in terms of eV?

ANSWER: 380 nm: 3.2 eV 780 nm: 1.6 eV