The drawing shows three energy levels of a laser that are involved in the lasing action. These levels are analogous to the levels in the Ne atoms of a He-Ne laser. The E2 level is a metastable level, and the E0 level is the ground state. The difference between the energy levels of the laser is shown in the drawing. (a) What energy (in eV per electron) must an external source provide to start the lasing action? (b) What is the wavelength of the laser light? (c) In what region of the electromagnetic spectrum does the laser light lie ?
To answer these questions, we need to understand the energy levels and their transitions in a laser system.
(a) To start the lasing action, an external source needs to provide energy equal to the energy difference between the two levels involved in the laser transition. In this case, the drawing shows the energy difference between E2 and E1 levels, which is the energy required to excite the electrons from the ground state to the metastable state. Let's denote this energy difference as ΔE.
To calculate the energy in electron volts (eV) per electron, we need to convert the energy difference to electron volts using the conversion factor 1 eV = 1.6 × 10^-19 Joules.
So, the energy required to start the lasing action (ΔE) can be calculated as:
ΔE (in eV) = ΔE (in Joules) / (1.6 × 10^-19)
(b) The wavelength of the laser light can be calculated using the formula:
λ = c / ν
where λ is the wavelength, c is the speed of light (approximately 3 × 10^8 m/s), and ν is the frequency of the laser light.
The frequency ν can be calculated using the energy difference ΔE:
ΔE = h * ν
where h is the Planck's constant (approximately 6.63 × 10^-34 J·s).
Solving for ν:
ν = ΔE / h
Now, substituting the value of ν into the wavelength formula, we get:
λ = c / (ΔE / h)
(c) Once we obtain the wavelength of the laser light, we can determine the region of the electromagnetic spectrum in which it lies. Different regions of the spectrum have different ranges of wavelengths, such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
To identify the region of the electromagnetic spectrum, we can refer to the wavelength values and compare them with the typical ranges for different regions.
Now let's calculate the answers step by step:
(a) First, we need the actual values of the energy difference (ΔE) and the Planck's constant (h) from the drawing or any other given information.
(b) Using the energy difference ΔE, we calculate the frequency ν using the formula ν = ΔE / h.
Then, using the speed of light (c) and the frequency (ν), we calculate the wavelength λ using the formula λ = c / ν.
(c) Once we have the wavelength λ, we compare it with the typical ranges for different regions of the electromagnetic spectrum to determine where the laser light lies.
Please provide the values for the energy difference ΔE and the Planck's constant h from the drawing or any other given information so that I can proceed with the calculations.