To calculate the number of photons required to raise the temperature of water, we need to use the equation:
E = n * h * c / λ
Where:
E is the energy of one photon
n is the number of photons
h is Planck's constant (6.626 x 10^-34 J s)
c is the speed of light (3.00 x 10^8 m/s)
λ is the wavelength of light in meters
First, we need to convert the wavelength from millimeters to meters. In this case, 3.00 mm is equal to 0.003 m.
Next, we can calculate the energy of one photon using the equation:
E = h * c / λ
E = (6.626 x 10^-34 J s) * (3.00 x 10^8 m/s) / 0.003 m
E ≈ 6.625 x 10^-22 J
Now we can calculate the number of photons using the equation:
E = n * (6.625 x 10^-22 J)
To raise the temperature of water, we need to calculate the heat energy required. The specific heat capacity of water is approximately 4.18 J/g°C.
The heat energy required can be calculated by using the equation:
Q = m * c * ΔT
Where:
Q is the heat energy
m is the mass of water in grams
c is the specific heat capacity of water
ΔT is the temperature change in °C
Given:
Mass of water (m) = 2.54 g
Temperature change (ΔT) = 1.00 °C
Specific heat capacity of water (c) = 4.18 J/g°C
Q = (2.54 g) * (4.18 J/g°C) * (1.00 °C)
Q ≈ 10.58 J
Finally, we can calculate the number of photons (n) using the equation:
10.58 J = n * (6.625 x 10^-22 J)
n ≈ 1.598 x 10^21 photons
Therefore, approximately 1.598 x 10^21 photons with a wavelength of 3.00 mm would need to be absorbed by 2.54 g of water to raise its temperature by 1.00 °C.