Given a system with 868 nm of wavelength, if N2/N1 is 0.62, calculate the flux of photons, intensity, absorption, and gain of atoms.

Steps to Solve

1. Convert Wavelength to Meters

To use the wavelength in calculations, convert from nanometers to meters.

$$ \text{Wavelength} = 868 , \text{nm} = 868 \times 10^{-9} , \text{m} $$

2. Calculate the Energy of a Photon

Using the formula for the energy of a photon:

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

where

• ( h ) is Planck's constant ((6.626 \times 10^{-34} , \text{Js})),
• ( c ) is the speed of light ((3 \times 10^8 , \text{m/s})),
• ( \lambda ) is the wavelength in meters.

Substituting the values:

$$ E = \frac{(6.626 \times 10^{-34})(3 \times 10^8)}{868 \times 10^{-9}} $$

3. Relate the Population Ratio to Gain and Absorption

The gain ( G ) is related to the population inversion ratio ( \frac{N_2}{N_1} ):

$$ G = \frac{N_2 - N_1}{N_1} \cdot \text{gain constant} $$

Given ( N_2/N_1 = 0.62 ):

Let ( N_1 = 1 ), then ( N_2 = 0.62 ).

Now:

$$ G = 0.62 - 1 = -0.38 $$

4. Calculate the Intensity and Flux of Photons

Intensity ( I ) is typically proportional to the flux ( \Phi ) and can be expressed as:

$$ I = \Phi \cdot E $$

You would need the specific flux value to calculate this further.

5. Discuss Absorption

Absorption can be calculated using:

$$ A = \frac{N_1}{N_1 + N_2} $$

Using our current values:

$$ A = \frac{1}{1 + 0.62} = \frac{1}{1.62} $$