Respuesta :
Given:
The time duration of the operation of the laser is t = 19.76 s
The power of the laser is P = 4.54 W
The wavelength of the red laser is
[tex]\begin{gathered} \lambda=661.98\text{ nm} \\ =\text{ 661.98 }\times10^{-9}\text{ m} \end{gathered}[/tex]Required: The number of photons.
Explanation:
In order to calculate the number of photons, first, we need to calculate the total energy of the photons.
The total energy of the photons can be calculated as
[tex]\begin{gathered} P=\frac{E}{t} \\ E=\text{ P }\times t \\ =4.54\times19.76\text{ s} \\ =89.71\text{ J} \end{gathered}[/tex]The energy of one photon is given by the formula
[tex]E_p=\frac{hc}{\lambda}[/tex]Here, h is the Planck's constant whose value is
[tex]h\text{ = 6.626}\times10^{-34\text{ }}Js[/tex]c is the speed of light whose value is
[tex]c=3\times10^8\text{ m/s}[/tex]On substituting the values, the energy of one photon will be
[tex]\begin{gathered} E_p=\frac{6.626\times10^{-34}\times3\times10^8}{661.98\times10^{-9}} \\ =3\times10^{-19}\text{ J} \end{gathered}[/tex]The number of photons can be calculated as
[tex]\begin{gathered} n=\frac{Total\text{ energy }}{energy\text{ of one photon}} \\ =\text{ }\frac{89.71}{3\times10^{-19}} \\ =2.99\times10^{20}\text{ photons} \end{gathered}[/tex]Final Answer: There are 2.99e20 photons during the operation of the red laser pointer.
