How does energy relate to wavelength and frequency?

1 Answer
Oct 1, 2015

Generally high frequency & small wavelength correspond to a higher energy state.

Explanation:

The energy of a photon is
#E=hf=hc/\lambda#
where #h# is Planck's constant
#\quad\quad\quad\quad\quadf# is the frequency of the light.
#\quad\quad\quad\quad\quad\lambda# is the wavelength of the light.
#\quad\quad\quad\quad\quadc# is the speed of light.

Ex) Blue light has a wavelength of #\approx 440#nm and red light has a wavelength of #\approx 680#nm. Since the blue light has a smaller wavelength (and hence a larger frequency #\quadf=c/\lambda#), a photon of blue light carries more energy than a photon of red light.


In quantum mechanics particle states are represented by wave functions. The momentum associated with a state is #p=h/\lambda#

The classical kinetic energy of the state is #E=p^2/(2m)=h^2/(2m\lambda^2)#

Again smaller wavelength corresponds to a greater energy.