A pushed dye laser emits light of wavelength 585 nm. Because this wavelength is strongly absorbed by the haemoglobin in the blood, the method is especially effective for removing various types of blemishes due to blood. To get a reasonable estimate of the power required for such laser surgery, we can model the blood as having the same specific heat and geat of vaporization as water. [`S=4.2xx10^(3)J(kgK)^(-1)`,`L=2.25xx10^(6)Jkg`]
Q. Suppose that each pulse must remove 2μg of blood by evaporating it starting at 30∘C.The number of photons that each pulse delivers to the blemish is

Options

A. `1.5xx10^(16)`
B. `1.5xx10^(8)`
C. `3xx10^(16)`
D. `3xx10^(8)`

Explanation

To solve the problem, we need to determine the number of photons emitted by a laser pulse that can evaporate 2 μg of blood starting at 30°C. We will use the specific heat and latent heat of vaporization of water to calculate the energy required for this process.

### Step-by-Step Solution:

1. **Convert Mass from Micrograms to Kilograms**:
\[ m = 2 \, \mu g = 2 \times 10^{-6} \, g = 2 \times 10^{-9} \, kg \]

2. **Calculate the Temperature Change (ΔT)**:
The blood needs to be heated from 30°C to 100°C (the boiling point of water).
\[ \Delta T = 100°C - 30°C = 70°C \]

3. **Use the Specific Heat Formula to Calculate Sensible Heat (Q_sensible)**:
The formula for sensible heat is:
\[ Q_{\text{sensible}} = m \cdot S \cdot \Delta T \]
Where:
- \( S = 4.2 \times 10^3 \, J/(kg \cdot K) \) (specific heat of water)
- \( m = 2 \times 10^{-9} \, kg \)
- \( \Delta T = 70 \, K \)

Substituting the values:
\[ Q_{\text{sensible}} = (2 \times 10^{-9}) \cdot (4.2 \times 10^3) \cdot (70) \]
\[ Q_{\text{sensible}} = 5.88 \times 10^{-5} \, J \]

4. **Calculate the Latent Heat (Q_latent)**:
The formula for latent heat is:
\[ Q_{\text{latent}} = m \cdot L \]
Where:
- \( L = 2.25 \times 10^6 \, J/kg \) (latent heat of vaporization)

Substituting the values:
\[ Q_{\text{latent}} = (2 \times 10^{-9}) \cdot (2.25 \times 10^6) \]
\[ Q_{\text{latent}} = 4.5 \times 10^{-3} \, J \]

5. **Calculate Total Energy Required (Q_total)**:
The total energy required to evaporate the blood is the sum of sensible and latent heat:
\[ Q_{\text{total}} = Q_{\text{sensible}} + Q_{\text{latent}} \]
\[ Q_{\text{total}} = 5.88 \times 10^{-5} + 4.5 \times 10^{-3} \]
\[ Q_{\text{total}} \approx 4.56 \times 10^{-3} \, J \]

6. **Calculate the Energy of One Photon (E_photon)**:
The energy of a photon can be calculated using the formula:
\[ E_{\text{photon}} = \frac{hc}{\lambda} \]
Where:
- \( h = 6.63 \times 10^{-34} \, J \cdot s \) (Planck's constant)
- \( c = 3 \times 10^8 \, m/s \) (speed of light)
- \( \lambda = 585 \, nm = 585 \times 10^{-9} \, m \)

Substituting the values:
\[ E_{\text{photon}} = \frac{(6.63 \times 10^{-34}) \cdot (3 \times 10^8)}{585 \times 10^{-9}} \]
\[ E_{\text{photon}} \approx 3.39 \times 10^{-19} \, J \]

7. **Calculate the Number of Photons (N)**:
The number of photons delivered in each pulse can be calculated as:
\[ N = \frac{Q_{\text{total}}}{E_{\text{photon}}} \]
Substituting the values:
\[ N = \frac{4.56 \times 10^{-3}}{3.39 \times 10^{-19}} \]
\[ N \approx 1.35 \times 10^{16} \]

### Final Answer:
The number of photons that each pulse delivers to the blemish is approximately \( 1.35 \times 10^{16} \).