How many photons are produced in a laser pulse of 0.756 J at 571 nm?
The Correct Answer and Explanation is:
To determine the number of photons produced in a laser pulse of 0.756 J at a wavelength of 571 nm, we need to relate the energy of the pulse to the energy of each photon and then calculate the number of photons.
Step-by-Step Solution
- Calculate the Energy of a Single Photon:
The energy (( E )) of a photon is given by: [
E = \frac{hc}{\lambda}
] where:
- ( h ) is Planck’s constant (( 6.626 \times 10^{-34} ) J·s),
- ( c ) is the speed of light (( 3.00 \times 10^8 ) m/s),
- ( \lambda ) is the wavelength (571 nm or ( 571 \times 10^{-9} ) m). Substituting these values: [
E = \frac{(6.626 \times 10^{-34} \text{ J·s}) \times (3.00 \times 10^8 \text{ m/s})}{571 \times 10^{-9} \text{ m}}
] Solving for ( E ), we get: [
E \approx 3.48 \times 10^{-19} \text{ J}
]
- Determine the Number of Photons:
The total energy of the pulse is 0.756 J. To find the number of photons (( N )), we divide the total energy by the energy per photon: [
N = \frac{\text{Total energy of pulse}}{\text{Energy of one photon}} = \frac{0.756 \text{ J}}{3.48 \times 10^{-19} \text{ J}}
] Solving for ( N ), we get: [
N \approx 2.17 \times 10^{18} \text{ photons}
]
Explanation
This calculation uses fundamental quantum physics principles. Each photon in a laser pulse carries a discrete packet of energy, directly proportional to the frequency of light (or inversely proportional to wavelength, as seen in our equation). By determining the energy of a single photon at 571 nm, we found how much energy each individual photon contributes. Dividing the total energy of the pulse by this value gives the count of photons required to make up the laser’s total energy.
Thus, for a laser pulse of 0.756 J at 571 nm, approximately ( 2.17 \times 10^{18} ) photons are produced. This high photon number reflects the intensity and concentration of energy typically found in laser pulses, a feature that makes lasers effective in a wide array of applications, from medical procedures to data communication.