**The Number of Photons of Light with a Given Wave Number in an Energy Source**

To understand the number of photons of light with a specific wave number in an energy source, we need to delve into the concepts of wave number, photons, and energy sources. Let's break down the topic into the following sections:

**Wave Number:**
The wave number, denoted by 'x,' is a fundamental property of light waves. It represents the spatial frequency of a wave, defined as the number of wave cycles per unit distance. Wave number is usually measured in reciprocal meters (m⁻¹) or centimeters (cm⁻¹).

**Photons:**
Light is composed of tiny particles called photons. Photons are elementary particles that have both wave-like and particle-like properties. Each photon carries a specific amount of energy that depends on its frequency or wave number. The energy of a photon is given by the equation E = hν, where E represents energy, h is Planck's constant (6.626 x 10⁻³⁴ J·s), and ν is the frequency of the light wave.

**Energy Source:**
An energy source refers to any system or device that emits or produces energy in the form of light. Examples of energy sources include light bulbs, lasers, the Sun, etc. These sources emit photons with different frequencies or wave numbers, depending on their nature and operation.

**Calculating the Number of Photons:**
To determine the number of photons of light with a wave number x in a given energy source, we need to consider the relationship between energy, wave number, and the number of photons.

1. Determine the energy associated with the given wave number x using the equation E = hν, where ν is related to wave number by the equation ν = c/x. Here, c represents the speed of light (3 x 10⁸ m/s).

2. Calculate the energy E associated with the wave number x.

3. Divide the total energy available in the energy source (in joules, J) by the energy of a single photon (E) to obtain the number of photons. This can be represented as the equation: Number of Photons = Total Energy / Energy of a Single Photon.

By following these steps, you can determine the number of photons of light with a specific wave number x in a given energy source. Remember that the energy source must emit photons within the desired wave number range for accurate calculations.