A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?

Verified step by step guidance

1. Calculate the energy of one photon using the equation $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{Js}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength of the photon (532 nm converted to meters).
2. Convert the energy of the laser pulse from millijoules to joules.
3. Divide the total energy of the laser pulse by the energy of one photon to find the number of photons. Use the formula $N = \frac{E_{\text{total}}}{E_{\text{photon}}}$, where $N$ is the number of photons, $E_{\text{total}}$ is the total energy of the pulse, and $E_{\text{photon}}$ is the energy of one photon.
4. Ensure the units are consistent when performing the calculations, particularly converting nm to meters for wavelength and mJ to J for energy.
5. Check the calculation for accuracy by verifying the units cancel appropriately, leaving a unitless count of photons.

Key Concepts

Photon Energy

The energy of a single photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. This relationship shows how the energy of photons is inversely proportional to their wavelength.

Total Energy of the Laser Pulse

The total energy of the laser pulse is given as 3.85 mJ, which can be converted to joules (1 mJ = 0.001 J). This total energy represents the cumulative energy of all the photons emitted in the pulse, and is essential for determining the number of photons present.

Calculating the Number of Photons

To find the number of photons in the laser pulse, divide the total energy of the pulse by the energy of a single photon. This calculation provides the total count of photons, illustrating the relationship between energy and the quantized nature of light.