Recap on dispersion relation for Lecture 6 Friday 2nd March, 2012

After class, Vincent and friends came and talked to me about the dispersion relation. He needed to verify about my derivation in class:
$\inline \lambda = \frac c \nu ~~~~~(1.1)$
We want to prove that this is can be related to Energy (eV) with the wavelength, $\inline \lambda$ :

$\inline Energy (eV) = \frac {1.24} {\lambda(\mu m)}$

If we multiply numerator and denominator by Planck's constant, $\inline h$ Equation (1.1) becomes
$\inline \lambda = \frac {hc} {h \nu} ~~~~~(1.2)$
Rearrange the expression, we have

$\inline {h \nu} = \frac {hc} {\lambda} ~~~~~(1.3)$

The left side of Equation (1.3) is in Joules (J). Since $\inline 1~eV= 1.6\displaystyle \times 10^{-19}~J$ , we have

$\inline \frac {h \nu} q = \frac {hc} {q \lambda} ~~~~~(1.4)$

The left side is now the Energy in eV, and substituting $\inline h=6.63 \times 10^{-34}~J-s, c=3 \times 10^{8}~\frac m s, \emph{and} ~q=1.6 \times 10^{-19}~C$ , we have

$\inline Energy (eV) = \frac {1.24} {\lambda(\mu m)}$

Recap on dispersion relation for Lecture 6 Friday 2nd March, 2012

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