Question

Calculate the energy corresponding to light of wavelength 45nm?

Answer 1

To solve this question, we have to use the formula for the energy of a photon. Energy of a photon is given by the product of Planck's constant and speed of light divided by the wavelength of the photon. Wavelength of the photon is given to us. Using this in the energy formula, we can easily solve this.

Formula used:
$E=\dfrac{hc}{\lambda }$

Complete step by step solution:
Here, we are asked to find the energy of the photon having a wavelength of 45 nm. Energy of a photon according to de broglie hypothesis is inversely proportional to its wavelength. Energy is given by the formula,
$E=\dfrac{hc}{\lambda }$
Where,
$h$ is planck's constant having the value
$h = 6.626\times {{10}^{-34}}Js$ .
$c$ is the speed of light in vacuum
and $\lambda$ is the wavelength of the photon.
Product of planck's constant and speed of light in eV.nm is given as,
$1242\text{ }eV.nm$.
Now, substituting the values in the equation,
$\begin{aligned} & E=\dfrac{hc}{\lambda } \\\ & \Rightarrow E=\dfrac{1242}{45} \\\ & \therefore E=27.6\text{ }eV \\\ \end{aligned}$
Therefore, energy corresponding to light of wavelength 45nm is $27.6\text{ }eV$.

Note: Photons can be described as really small particles that do not have charge on them which keep on moving with some velocity. Photons also do not have any rest mass. Energy of a photon can be written as the product of Planck's constant and frequency of the photon. The energy of a photon can be expressed in different units like joules or electron volts.