### Mathematical Relationships for Light

This is another reference book page, which may become useful throughout the course, especialy when we talk about properties of light and light energy conversion. This content is for your fiuture reference (you will not be tested on it during orientation).

#### Relation between wave length, frequency, and speed of light

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

$$\lambda =\frac{c}{\nu}$$

where c= speed of light in a vacuum ($\approx 3\times {10}^{17}\frac{nm}{s}$ )

#### Dependence of radiation energy on frequency

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

$${E}_{p}=h\cdot \nu \frac{hc}{\lambda}$$

where h=Planck's constant ($\approx 4.1357\times {10}^{-15}eV\cdot s$)

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:

$${E}_{p}=\frac{1239.8\text{}eV\cdot nm}{\lambda}$$

or

$$\lambda =\frac{1239.8eV\cdot nm}{Ep}$$

**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:

$${E}_{p}=\frac{1234.5\text{}eV\cdot nm}{\lambda}$$

or

$$\lambda =\frac{1234.5\text{}eV\cdot nm}{{E}_{p}}$$

#### 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?

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

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