Question

How many photons are emitted during 19.76 s of operation of a red laser pointer? The device outputs 4.54 Watts at a 661.98 nm wavelength.

Answer 1

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

`\begin{gathered} \lambda=661.98\text{ nm} \\ =\text{ 661.98 }*10^(-9)\text{ m} \end{gathered}`

Required: The number of photons.

Step-by-step 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

`\begin{gathered} P=(E)/(t) \\ E=\text{ P }* t \\ =4.54*19.76\text{ s} \\ =89.71\text{ J} \end{gathered}`

The energy of one photon is given by the formula

`E_p=(hc)/(\lambda)`

Here, h is the Planck's constant whose value is

`h\text{ = 6.626}*10^{-34\text{ }}Js`

c is the speed of light whose value is

`c=3*10^8\text{ m/s}`

On substituting the values, the energy of one photon will be

`\begin{gathered} E_p=(6.626*10^(-34)*3*10^8)/(661.98*10^(-9)) \\ =3*10^(-19)\text{ J} \end{gathered}`

The number of photons can be calculated as

`\begin{gathered} n=\frac{Total\text{ energy }}{energy\text{ of one photon}} \\ =\text{ }(89.71)/(3*10^(-19)) \\ =2.99*10^(20)\text{ photons} \end{gathered}`

Final Answer: There are 2.99e20 photons during the operation of the red laser pointer.