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 power output of laser in time 450μs must be

Options

A. 5.5 W
B. 11 W
C. 16.5 W
D. 22 W

Explanation

To solve the problem, we need to calculate the power output of the laser required to evaporate 2 μg of blood starting at 30°C in a time of 450 μs. We will use the specific heat and latent heat values provided for the calculations.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of blood (m) = 2 μg = \(2 \times 10^{-6}\) g = \(2 \times 10^{-9}\) kg
- Specific heat (S) = \(4.2 \times 10^{3}\) J/(kg·K)
- Latent heat (L) = \(2.25 \times 10^{6}\) J/kg
- Initial temperature (T_initial) = 30°C
- Final temperature (T_final) = 100°C (for evaporation)
- Time (t) = 450 μs = \(450 \times 10^{-6}\) s

2. **Calculate the Temperature Change (ΔT):**
\[ \Delta T = T_{final} - T_{initial} = 100°C - 30°C = 70°C \]

3. **Calculate the Energy Required to Raise the Temperature:**
The energy required to raise the temperature of the blood can be calculated using the formula:
\[ Q_1 = m \cdot S \cdot \Delta T \]
Substituting the values:
\[ Q_1 = (2 \times 10^{-9} \text{ kg}) \cdot (4.2 \times 10^{3} \text{ J/(kg·K)}) \cdot (70 \text{ K}) \]
\[ Q_1 = 2 \times 10^{-9} \cdot 4.2 \times 10^{3} \cdot 70 = 5.88 \times 10^{-5} \text{ J} \]

4. **Calculate the Energy Required for Vaporization:**
The energy required to vaporize the blood is given by:
\[ Q_2 = m \cdot L \]
Substituting the values:
\[ Q_2 = (2 \times 10^{-9} \text{ kg}) \cdot (2.25 \times 10^{6} \text{ J/kg}) \]
\[ Q_2 = 4.5 \times 10^{-3} \text{ J} \]

5. **Calculate the Total Energy Required (Q_total):**
\[ Q_{total} = Q_1 + Q_2 \]
\[ Q_{total} = 5.88 \times 10^{-5} \text{ J} + 4.5 \times 10^{-3} \text{ J} = 4.55588 \times 10^{-3} \text{ J} \]

6. **Calculate the Power Output of the Laser:**
Power (P) is defined as energy per unit time:
\[ P = \frac{Q_{total}}{t} \]
Substituting the values:
\[ P = \frac{4.55588 \times 10^{-3} \text{ J}}{450 \times 10^{-6} \text{ s}} = 10.1 \text{ W} \]

### Final Answer:
The power output of the laser must be approximately **10.1 Watts**.