A 10.4 in^2 tattoo is removed with a laser that delivers 0.96 Watts/cm^2 of energy per pulse at a wavelength of 1,064 nm. If the tattoo removal process takes place continuously for a 25 min session, how many photons are are delivered in a pulse of this laser?

To find the number of photons delivered in a single pulse of the laser, we can follow these steps:

### Step 1: Convert units to consistent ones
We need to convert the units for power, area, and time so that they are compatible.

- **Tattoo area**: \(10.4 \, \text{in}^2\)
  - Convert inches to cm: \(1 \, \text{in} = 2.54 \, \text{cm}\)
  - Area in cm²:
  \[
  10.4 \, \text{in}^2 \times (2.54 \, \text{cm/in})^2 = 67.1 \, \text{cm}^2
  \]

- **Laser intensity**: \(0.96 \, \text{W/cm}^2\)
  - The laser delivers \(0.96 \, \text{W/cm}^2\) of power per unit area.

### Step 2: Total power delivered by the laser
To find the total power delivered by the laser on the tattoo, we multiply the laser intensity by the area:

\[
\text{Total power} = 0.96 \, \text{W/cm}^2 \times 67.1 \, \text{cm}^2 = 64.4 \, \text{W}
\]

### Step 3: Energy of a photon
The energy of a photon \(E\) is related to its wavelength \(\lambda\) by the equation:

\[
E = \frac{h c}{\lambda}
\]
where:
- \(h = 6.626 \times 10^{-34} \, \text{J·s}\) is Planck's constant,
- \(c = 3.00 \times 10^8 \, \text{m/s}\) is the speed of light,
- \(\lambda = 1,064 \, \text{nm} = 1.064 \times 10^{-6} \, \text{m}\) is the wavelength of the laser.

Now, calculate the energy of a single photon:
\[
E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{1.064 \times 10^{-6}} \, \text{J}
= 1.87 \times 10^{-19} \, \text{J}
\]

### Step 4: Number of photons per pulse
To find the number of photons delivered per pulse, we divide the total energy per pulse by the energy of a single photon.

First, find the total energy delivered per second (since \(1 \, \text{W} = 1 \, \text{J/s}\)):

\[
\text{Total energy per second} = 64.4 \, \text{J/s}
\]

Now, divide this by the energy of a single photon to get the number of photons per second:

\[
\text{Photons per second} = \frac{64.4 \, \text{J}}{1.87 \times 10^{-19} \, \text{J}} = 3.44 \times 10^{20} \, \text{photons/second}
\]

The question specifically asks for the number of photons **per pulse**. Assuming the laser operates with continuous pulses and the session lasts 25 minutes, we don't have explicit pulse duration data. If pulse rate or duration was known, the result could be refined for per pulse photons.

Would you like details or have any questions on this? 

Here are 5 related questions:
1. How does the energy of a photon change with wavelength?
2. How would the number of photons change if the wavelength was doubled?
3. What would happen to the number of photons if the laser's power increased to 2.0 Watts/cm²?
4. How could the efficiency of the tattoo removal process be improved in this context?
5. What are other applications of lasers with similar wavelengths?

**Tip:** When calculating photon energy, always ensure you’re working with SI units (meters for wavelength).

A 10.4 in^2 tattoo is removed with a laser that delivers 0.96 Watts/cm^2 of energy per pulse at a wavelength of 1,064 nm. If the tattoo removal process takes place continuously for a 25 min session, how many photons are delivered in a pulse of this laser?

Learn how to calculate the number of photons delivered in a single pulse of a laser during a tattoo removal process. The solution involves converting area units, calculating total power, and using Planck's equation to determine photon energy. Suitable for undergraduate physics or engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation