If the power of light is 10 kW and the wavelength is 300 nm, find the number of photons per second.

Steps to Solve

1. Determine the energy of a single photon

The energy $E$ of a photon can be calculated using the formula:

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

where:

• $h$ is Planck's constant ($6.626 \times 10^{-34} , \text{Js}$),
• $c$ is the speed of light in a vacuum ($3.00 \times 10^8 , \text{m/s}$), and
• $\lambda$ is the wavelength ($300 , \text{nm}$, which is $300 \times 10^{-9} , \text{m}$).

2. Calculate the energy per photon

Substituting in the values:

$$ E = \frac{(6.626 \times 10^{-34} , \text{Js})(3.00 \times 10^8 , \text{m/s})}{300 \times 10^{-9} , \text{m}} $$

Calculate this value to find the energy of a single photon.

3. Calculate the total energy emitted per second

Using the power of the light source ($P = 10 , \text{kW} = 10,000 , \text{W}$):

$$ P = \frac{\text{Total Energy}}{\text{Time}} $$

Since time is 1 second, the total energy emitted per second is equal to the power:

$$ \text{Total Energy} = 10,000 , \text{J} $$

4. Find the number of photons emitted per second

The number of photons $N$ emitted per second can be found using:

$$ N = \frac{\text{Total Energy}}{E} $$

Now substitute in the total energy from the previous step and the energy per photon from step 2.

5. Calculate the final value

Perform the calculation:

$$ N = \frac{10,000 , \text{J}}{E} $$

This will give you the number of photons emitted per second.