The number of photons of light having wave number x in 1J of energy source is (Planck's constant =h, velocity of light = c)

Options

A. hcx
B. `hc//x`
C. `(x)/(hc)`
D. `(1)/(hx)`

Explanation

To solve the problem of finding the number of photons of light having wave number \( x \) in 1 Joule of energy, we can follow these steps:

### Step 1: Understand the relationship between energy, number of photons, and wave number

The energy \( E \) of a photon can be expressed in terms of its wave number \( x \):
\[ E = n \cdot \frac{hc}{\lambda} \]
where:
- \( n \) is the number of photons,
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength.

### Step 2: Relate wave number to wavelength

The wave number \( x \) is defined as:
\[ x = \frac{1}{\lambda} \]
This means that we can express the wavelength \( \lambda \) in terms of wave number:
\[ \lambda = \frac{1}{x} \]

### Step 3: Substitute the wavelength in the energy equation

Substituting \( \lambda \) into the energy equation gives:
\[ E = n \cdot \frac{hc}{\frac{1}{x}} = n \cdot hc \cdot x \]

### Step 4: Solve for the number of photons \( n \)

Rearranging the equation to solve for \( n \):
\[ n = \frac{E}{hcx} \]

### Step 5: Substitute the given energy

We know that the total energy \( E \) is 1 Joule:
\[ n = \frac{1}{hcx} \]

### Conclusion

Thus, the number of photons of light having wave number \( x \) in 1 Joule of energy is:
\[ n = \frac{1}{hcx} \]