Question

How does energy relate to wavelength and frequency?

Answer 1

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.

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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.