Question

What is the energy of a transition capable of producing light of wavelength \(10.6 \mu \mathrm{m} ?\) (This is the wavelength of light associated with a commonly available infrared laser.)

Short answer

Question: Calculate the energy of a transition capable of producing light with a wavelength of 10.6 μm. Answer: The energy of the transition is approximately 1.87e-20 Joules.

Step-by-step solution

Write the formula for energy of a photon

We'll use the formula E = (hc)/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

Convert wavelength to meters

Given the wavelength in micrometers (μm), we need to convert it to meters (m). Since 1 μm = 1e-6 m, we have 10.6 μm = 10.6 * 1e-6 m = 1.06e-5 m.

Provide the values of Planck's constant and the speed of light

Planck's constant (h) is about 6.626e-34 Js, and the speed of light (c) is approximately 3.00e8 m/s.

Plug the values into the formula

Now, we can plug the values of h, c, and λ into the formula to find the energy (E) of the transition: E = (6.626e-34 Js × 3.00e8 m/s)/(1.06e-5 m).

Calculate the energy

After plugging the values into the formula, we can calculate the energy: E = (1.9878e-25 Js²)/(1.06e-5 m) ≈ 1.87e-20 J. So, the energy of the transition capable of producing light of wavelength 10.6 μm is approximately 1.87e-20 Joules.