A Closer Look at Photons and Atom Population in Lasers

What is the number of photons per second emitted by a thermal source of light and a small gas laser at a wavelength of 500 nm? How can we calculate the fraction of atoms in the upper state of a He-Ne laser at 300 K?

Number of Photons per Second Calculation:

The thermal source of light emits 10^9 photons per second of green light at 500 nm. A small gas laser with a power output of 1 mW at the same wavelength emits approximately 2.514 × 10^15 photons per second in the beam. To calculate the number of photons per second, we use the formula: Number of photons per second = Power / Energy per photon. First, we determine the energy per photon at 500 nm (green light) using the Energy = Planck's constant * speed of light / wavelength formula. Plugging in the values, we get 3.9737 × 10^-19 J. For the thermal source, the number of photons per second is 10^9, while for the small gas laser, it is approximately 2.514 × 10^15 photons per second.

Fraction of Atoms in the Upper State Calculation:

In the He-Ne laser at 300 K, approximately 2.23 × 10^-31 fraction of atoms is in the upper state. This can be calculated using the Boltzmann distribution formula: N2/N1 = exp(-ΔE / (k * T)), where N2/N1 is the ratio of atoms in the upper state to the lower state, ΔE is the energy difference between the states, k is the Boltzmann constant, and T is the temperature in Kelvin. Given the energy difference ΔE between the two states at 633 nm as 3.141 × 10^-19 J, the calculation results in a fraction of atoms in the upper state in the He-Ne laser at 300 K as approximately 2.23 × 10^-31.

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