Question

A laser pulse with wavelength 550 nm contains 4.40 mJ of energy. How many photons are in the laser pulse?

Answer 1

Answer:- $1.22*10^1^6photon$

Solution:- First of we calculate the energy of the laser pulse for it's given wavelength which actually the energy in joule per photon. After this the given energy value is divided by the calculated energy to find out the number of photons.

The calculations are done as:

For energy calculations the equation used is:

$E=\frac{hc}{\lambda }$

where, E is energy, h is planck's constant and $\lambda$ is the wavelength.

The values of the constants are as follows:

$h=6.626*10^-^3^4J.s$

$c=3.0*10^8\frac{m}{s}$

wavelength is given as 550 nm. We need to convert it to m.

$\lambda =550nm(\frac{10^-^9m}{1nm})$

$\lambda =5.5*10^-^7m$

Let's plug in the values in the equation to calculate E:

$E=\frac{(6.626*10^-^3^4J.s)(3.0*10^8\frac{m}{s})}{5.5*10^-^7m}$

$E=3.61*10^-^1^9J$

This is the energy for one photon. The given energy value is 4.40 mJ that is $4.40*10^-^3J$ .

let's divide this value by the calculated value to get the number of photons as:

$4.40*10^-^3J(\frac{1photon}{3.61*10^-^1^9J})$

= $1.22*10^1^6photon$

So, there would be $1.22*10^1^6photon$ photons in the laser pulse.

Answer 2

The elementary particle of the electromagnetic field is photons. In the laser pulse, the number of the photons are $1.22 \times 10^{16} \;\rm photons.$

What is energy?

The energy of the particle is defined by the ratio of the product of the speed of light and Planck's constant to the wavelength. It can be given as,

$\rm E = \rm \dfrac{hc}{\lambda}$

Given,

Planck's constant (h) = $6.626 \times 10^{-34} \;\rm Js$

Speed of light (c) = $3.0 \times 10^{8}\;\rm m/s$

Wavelength = $5.5 \times 10^{-7}\;\rm m$

Substituting values in the equation:

$\begin{aligned} \rm E &= \dfrac{6.626 \times 10^{-34} \times 3.0 \times 10^{8}}{ 5.5 \times 10^{-7}}\\\\&= 3.61 \times 10^{-19}\;\rm J\end{aligned}$

Hence, $3.61 \times 10^{-19}\;\rm J$ is the energy of one photon. The given energy of the laser pulse is 4.40 mJ.

The number of photons will be:

$\dfrac{4.40 \times 10^{-3}}{3.61 \times 10^{-19}} = 1.22 \times 10^{16} \;\rm photons.$

Therefore, $1.22 \times 10^{16}$ photons are present in the laser pulse.

Learn more about photons here:

https://brainly.com/question/5419328