Answer:
Step-by-step explanation:
To find the number of photons required to raise the temperature of 1.00 cm³ of flesh to 100°C and evaporate it using a carbon dioxide laser emitting infrared radiation with a wavelength of 10.6 μm, you can use the following steps:
Calculate the energy required to raise the temperature of 1.00 cm³ of flesh from its initial temperature to 100°C.
Calculate the energy required to vaporize the flesh at 100°C.
Find the total energy required.
Use the energy of a single photon at 10.6 μm to find the number of photons required.
Let's calculate it step by step:
Step 1: Calculate the energy required to raise the temperature.
The heat energy required to raise the temperature of a substance can be calculated using the formula:
Q = mcΔT
Where:
Q = heat energy (in Joules)
m = mass (in kg)
c = specific heat capacity (for water or flesh, which is close to water, it's about 4.18 J/g°C)
ΔT = change in temperature (in °C)
Converting the mass from cm³ to grams:
1 cm³ = 1 gram
So, 1.00 cm³ = 1.00 g
Now, we convert grams to kilograms:
1.00 g = 0.001 kg
ΔT = 100°C - initial temperature (assumed to be 0°C) = 100°C
Q = (0.001 kg) * (4.18 J/g°C) * (100°C) = 0.418 J
Step 2: Calculate the energy required to vaporize the flesh.
The energy required to vaporize 1 gram of water at 100°C is called the heat of vaporization and is approximately 2.25 x 10^6 J/kg.
So, for 1 gram (0.001 kg) of flesh:
Q_vaporization = (0.001 kg) * (2.25 x 10^6 J/kg) = 2250 J
Step 3: Find the total energy required.
Total energy required = Energy to raise temperature + Energy for vaporization
Total energy = 0.418 J + 2250 J = 2250.418 J
Step 4: Use the energy of a single photon to find the number of photons required.
The energy of a single photon can be calculated using the formula:
E = hc/λ
Where:
E = energy of a photon (in Joules)
h = Planck's constant (6.626 x 10^-34 J·s)
c = speed of light (approximately 3.00 x 10^8 m/s)
λ = wavelength (in meters)
Convert the wavelength from micrometers to meters:
10.6 μm = 10.6 x 10^-6 m
Now, calculate the energy of a single photon:
E = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (10.6 x 10^-6 m) = 1.877 x 10^-19 J
Finally, to find the number of photons required, divide the total energy by the energy of a single photon:
Number of photons = Total energy / Energy of a single photon
Number of photons = (2250.418 J) / (1.877 x 10^-19 J/photon)
Number of photons ≈ 1.197 x 10^21 photons
So, approximately 1.197 x 10^21 photons are required to raise the temperature of 1.00 cm³ of flesh to 100°C and evaporate it using the carbon dioxide laser.