Understanding Atomic Energy Level Difference and Light Intensity Amplification in Lasers

How can we calculate the atomic energy level difference of a laser medium based on its wavelength?

(a) To calculate the atomic energy level difference E2​−E1​, we can use the equation E=hc/λ, where E is the energy, h is the 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. Plugging in the given wavelength λ=633 nm (or 633 x 10^-9 m), we can calculate the atomic energy level difference.

Calculation of Atomic Energy Level Difference:

E = (6.626 x 10^-34 J·s) * (3 x 10^8 m/s) / (633 x 10^-9 m)

E ≈ 3.14 x 10^-19 J

Therefore, the atomic energy level difference is approximately 3.14 x 10^-19 J.

How can we determine the distance required to amplify the light intensity by 100 times in a laser medium with a specific gain?

(b) The exponential growth equation I=I0​e^Gx relates the initial intensity I0​, the gain G, the distance x, and the final intensity I. To find the distance x required to amplify the light intensity by 100 times, we rearrange the equation and solve for x.

Calculation of Distance for Light Intensity Amplification:

100 = e^(0.01/cm * x)

ln(100) = ln(e^(0.01/cm * x))

4.605 = 0.01/cm * x

Therefore, the distance x required to amplify the light intensity by 100 times is approximately 460.5 cm.