A ruby laser produces radiations of wavelength, `662.6nm` in pulse whose duration are `10^(-9)s`. If the laser produces `0.39 J` of energy per pulse, how many protons are produced in each pulse?

Options

A. `1.3xx10^9`
B. `1.3xx10^(18)`
C. `1.3xx10^(27)`
D. `3.9xx10^(18)`

Answer

To solve the problem of how many protons are produced in each pulse of a ruby laser, we can follow these steps:

### Step 1: Understand the relationship between energy, wavelength, and the number of photons.
The energy of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( E \) is the energy of a single photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the radiation.

### Step 2: Convert the wavelength from nanometers to meters.
Given the wavelength \( \lambda = 662.6 \, \text{nm} \):
\[ \lambda = 662.6 \times 10^{-9} \, \text{m} \]

### Step 3: Calculate the energy of a single photon.
Using the formula from Step 1, we can substitute the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{662.6 \times 10^{-9} \, \text{m}} \]

Calculating this gives:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{662.6 \times 10^{-9} \, \text{m}} \]
\[ E \approx 2.998 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the total energy produced in one pulse.
The total energy produced in one pulse is given as \( 0.39 \, \text{J} \).

### Step 5: Determine the number of photons produced in each pulse.
The number of photons \( n \) can be calculated using the formula:
\[ n = \frac{E_{\text{total}}}{E_{\text{photon}}} \]
Where:
- \( E_{\text{total}} = 0.39 \, \text{J} \)
- \( E_{\text{photon}} \) is the energy of a single photon calculated in Step 3.

Substituting the values:
\[ n = \frac{0.39 \, \text{J}}{2.998 \times 10^{-19} \, \text{J}} \]

Calculating this gives:
\[ n \approx 1.30 \times 10^{18} \]

### Conclusion:
The number of protons produced in each pulse is approximately \( 1.30 \times 10^{18} \).