Question

What is the energy of a photon with a wavelength of $700\text{ nm}$?

Answer 1

To solve this problem, we have to use the formula to calculate the energy of a photon. According to the formula, the energy of a photon is the product of Planck’s constant and speed of light divided by the wavelength of the photon. We are given with the wavelength of the photon; hence we could easily find out its energy.
Formula used: $E=\dfrac{hc}{\lambda }$

Complete step-by-step solution:
In the question we were asked to calculate the energy of the photon that has a wavelength of $700\text{ nm}$. The energy if a photon according to the De Broglie Hypothesis is inversely proportional to the wavelength of the photo and hence is given as follows:
$E=\dfrac{hc}{\lambda }$
Where, $h$ is the Planck’s constant and its value is $h=6.626\times {{10}^{-34}}\text{ Js}$,
$c$is the velocity of light and its value is $c=3\times {{10}^{8}}\text{ m}{{\text{s}}^{-1}}$,
And $\lambda$ is the wavelength of the photon which is given in the question as $\lambda =700\text{ nm}$.
Here, we know that the product of Planck’s constant and speed of light is $1242\text{ eV}\cdot \text{nm}$. Hence on substituting the values in the equation, we get the following:
$\begin{aligned} & E=\dfrac{1242}{700} \\\ & \Rightarrow E=1.77\text{ eV} \\\ \end{aligned}$
Thus, the energy of the photon whose wavelength is $700\text{ nm}$ will be $1.77\text{ eV}$.

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 also be written as the product of Planck’s constant and the frequency of the photon. The energy of the photon can be expressed in different units like Joules or electron volt.