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A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 μm. In 1.00 ms, this laser raised the temperature of 1.00 cm³ of flesh to 100C and evaporated it. How many photons were required? You may assume flesh has the same heat of vaporization as water.

User AllDayer
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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.

User Grish
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