A ruby laser emits an intense pulse of light that lasts a mere 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 500 mJ. What is the rate of photon emission, in photons per second, during the 10 ns that the laser is 'on'?

Verified step by step guidance

1. Determine the energy of a single photon using the formula: \( E_{photon} = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J·s} \)), \( c \) is the speed of light (\( 3.00 \times 10^8 \; \text{m/s} \)), and \( \lambda \) is the wavelength of the light (\( 690 \, \text{nm} = 690 \times 10^{-9} \; \text{m} \)).
2. Calculate the total number of photons emitted in one pulse by dividing the total energy of the pulse by the energy of a single photon: \( N = \frac{E_{pulse}}{E_{photon}} \), where \( E_{pulse} = 500 \, \text{mJ} = 500 \times 10^{-3} \, \text{J} \).
3. Determine the duration of the pulse in seconds: \( t = 10 \; \text{ns} = 10 \times 10^{-9} \; \text{s} \).
4. Calculate the rate of photon emission by dividing the total number of photons emitted by the duration of the pulse: \( R = \frac{N}{t} \), where \( N \) is the total number of photons and \( t \) is the pulse duration.
5. Express the final result for the rate of photon emission in photons per second, ensuring all units are consistent and properly simplified.

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 x 10^8 m/s), and λ is the wavelength in meters. For a ruby laser emitting light at 690 nm, this formula allows us to determine the energy of each photon emitted during the laser pulse.

Pulse Duration

The pulse duration refers to the time interval during which the laser emits light. In this case, the ruby laser emits light for 10 nanoseconds (ns), which is 10 x 10^-9 seconds. Understanding the duration is crucial for calculating the total number of photons emitted during this brief period, as it directly influences the rate of emission.

Photon Emission Rate

The photon emission rate is the number of photons emitted per second. It can be calculated by dividing the total energy emitted during the pulse by the energy of a single photon. This rate provides insight into the intensity of the laser and is essential for understanding the laser's performance and applications in various fields.