a certain ruby laser emits 2.5 j pulses of light of wavelenght 6940 angstrom .what is the minimum number of cromium ions in the ruby laser??

To determine the minimum number of chromium ions in a ruby laser that emits 2.5 joules of light pulses at a wavelength of 6940 angstroms, we need to understand the relationship between energy, wavelength, and the number of photons emitted. Let's break this down step by step.

Understanding Photon Energy

The energy of a single photon can be calculated using the formula:

E = hc / λ

Where:

• E = energy of a photon (in joules)
• h = Planck's constant (approximately 6.626 x 10^-34 J·s)
• c = speed of light (approximately 3.00 x 10⁸ m/s)
• λ = wavelength (in meters)

Converting Wavelength

First, we need to convert the wavelength from angstroms to meters. Since 1 angstrom is equal to 1 x 10^-10 meters:

6940 angstroms = 6940 x 10^-10 m = 6.94 x 10^-7 m

Calculating Photon Energy

Now, we can substitute the values into the energy formula:

E = (6.626 x 10^-34 J·s) * (3.00 x 10⁸ m/s) / (6.94 x 10^-7 m)

Calculating this gives:

E ≈ 2.86 x 10^-19 J

Finding the Number of Photons

Next, we need to find out how many photons are emitted in a pulse of 2.5 joules. This can be done using the formula:

N = Total Energy / Energy per Photon

Substituting the values we have:

N = 2.5 J / (2.86 x 10^-19 J)

Calculating this gives:

N ≈ 8.75 x 10¹⁸ photons

Determining Chromium Ions

In a ruby laser, each photon emitted corresponds to the transition of a chromium ion (Cr³⁺) from an excited state to a lower energy state. Therefore, the minimum number of chromium ions that must be present to produce this many photons is equal to the number of photons emitted, assuming each ion contributes to the emission of one photon.

Thus, the minimum number of chromium ions in the ruby laser is:

Approximately 8.75 x 10¹⁸ chromium ions

Summary

In summary, by calculating the energy of a single photon and then determining how many photons correspond to the total energy emitted in a pulse, we find that the ruby laser must contain at least 8.75 x 10¹⁸ chromium ions to produce a pulse of 2.5 joules at a wavelength of 6940 angstroms. This illustrates the fascinating interplay between energy, light, and the materials used in laser technology.