The speed of light, the wavelength of the laser light, and the frequency of the laser light are all related using the formula:
c = f λ, (1)
where c = 299, 792, 458 m/s ≈ 3 × 108 m/s is a constant of nature known as the speed of light.1 The energy of a photon is given by the formula:
Eph = hf, (2)
where h is a constant of nature known as Planck’s constant, named after German physicist Max Planck. Planck’s constant is a very small number, h = 6.626 × 10−34 Js. The units are joules times seconds, where joules is the unit of energy. The most important thing to emphasize here is that we have multiple ways to state the same property of a photon. If I tell you the wavelength of the light, you can immediately calculate the frequency of the light and the energy of the photons that make up that light. Since all three quantities are related by constants, an atomic physicist will claim that wavelength, frequency, and the energy of a photon are all the same thing. An atomic physicist might very well say, “the energy of the photon is 632 THz” and think nothing of it. It takes some practice to use “wrong” units to describe something! Imagine if you asked me my height, and I responded with 150 MHz. For physicists, there is nothing wrong with doing this since we would only be off by a constant of nature.
A common energy unit is inverse centimeters. For example, the statement, “The energy difference between the two states is 12,460 cm−1” is very common. For spectroscopists, this number means the same thing as 2.475 × 10−19 J. Converting
between the two numbers requires multiplying by the correct combination of the fundamental constants h and c. ... We can now make a new definition:
• Resonance frequency: When the frequency of the laser is just right to excite the atom from the ground state to an excited state, we call that the resonance frequency. We use the variable fr to represent resonance frequency. Since resonance frequency is a frequency, it uses units of Hz, MHz, GHz, or THz.
Common Misconception Power is not the same thing as energy. Power is the rate at which energy is exiting the laser. Imagine two laser beams with two different frequencies. The light from laser #1 has a higher frequency than the light from laser #2. We now know that the photons that make up laser #1 have more energy than the photons that make up laser #2. Power is how much energy is exiting the laser per second. If the same number of photons per second are leaving both lasers, laser #1 has a larger power. In math form, the power of a laser is:
P = NEph (3)
where N is how many photons per second that leave the laser and Eph = hf is the energy of a single photon. The unit for power is a watt, named in honor of Scottish chemist James Watt. A watt is shortened to W and is equivalent to joules per second. Imagine you have a 1 watt laser and a 10 watt laser that have photons with the same energy. The 10 watt laser emits 10 times as many photons per second as a 1 watt laser.
1- This is the speed of light in a vacuum. It is exactly 299, 792, 458 m/s.
