Question

How can I calculate the wavelength from energy?

Answer 1

Hint: As a first step you could recall the Planck’s law to get the energy of a photon in terms of frequency. Then you could recall the expression of frequency in terms of speed of light in vacuum (c) and wavelength of radiation $\lambda $. Now you could substitute this expression of frequency in the above expression to get the required relation.

Formula used:
Planck’s law,
$E=h\nu $
Expression for frequency,
$\nu =\dfrac{c}{\lambda }$

Complete Step by step solution:
In the question, we are asked the method to calculate the wavelength from energy.

This is actually a pretty simple derivation from Planck's equation. Max Planck found that energy of a photon is transferred as quanta. And the quantum energy could be given by the following relation,
$E=h\nu $ …………………………………………………. (1)
Where, $\nu $ is the frequency of radiation and h is the Planck’s constant which is known to have a value,
$h=6.626\times {{10}^{-34}}J-\sec $
Thus we could easily calculate the energy of photons using this relation.

Now you may recall that the frequency is related to wavelength as,
$\nu =\dfrac{c}{\lambda }$ …………………………………………………… (2)
Where, c is the speed of light in vacuum and $\lambda $ is the wavelength of the radiation.

Now, we could substitute (2) in (1) to get energy in terms of wavelength as,
$E=h\dfrac{c}{\lambda }$

Therefore, we found that wavelength of a photon can be found from its known energy using the following relation,
$\lambda =\dfrac{hc}{E}$

Note:
Max Planck found different particles to oscillate at different frequencies. Planck's law which is based on various observations of Max Planck states that the energy of the oscillation is proportional to the frequency. Also, Planck’s constant is known to have a great fundamental significance.