A particular microwave oven delivers 800 watts. (A watt is a unit of power, which is the joules of energy delivered, or used, per second.) If the oven uses microwave radiation of wavelength 12.2 cm, how many photons of this radiation are required to heat 1.25 g of water 1.00°C, assuming that all the photons are absorbed?
I would do this.
Energy of one photon of 12.2 cm
E = hc/wavelength. Remember wavelength must be in meters.
Then Energy needed to heat 1.25 g water =
q = mass H2O x specific heat water x delta T.
So how many photons must be used to acquire q.
Thanks Dr. Bob
To find the number of photons required to heat 1.25 g of water by 1.00°C, we need to follow these steps:
Step 1: Calculate the energy required to heat the water.
Step 2: Convert the energy from Joules to photons.
Let's start with step 1:
Step 1: Calculating the energy required to heat the water:
The formula to calculate the energy required to heat a substance is given by:
Q = mcΔT
Where:
Q is the energy in Joules,
m is the mass of the substance in grams,
c is the specific heat capacity of water (4.18 J/g°C),
ΔT is the change in temperature in degrees Celsius.
Given:
m = 1.25 g
c = 4.18 J/g°C
ΔT = 1.00°C
Q = (1.25 g) * (4.18 J/g°C) * (1.00°C)
Q = 5.225 J
Now, moving to step 2:
Step 2: Converting the energy from Joules to photons:
The energy of a photon is given by the equation:
E = hc/λ
Where:
E is the energy of a photon in Joules,
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 the microwave radiation in meters.
Given:
λ = 12.2 cm = 0.122 m
E = 5.225 J
h = 6.626 x 10^-34 J*s
c = 3.00 x 10^8 m/s
Rearranging the equation, we get:
N = E / (hc/λ)
Substituting the values:
N = 5.225 J / [(6.626 x 10^-34 J*s) * (3.00 x 10^8 m/s) / 0.122 m]
Simplifying:
N = 5.225 J * (0.122 m) / [(6.626 x 10^-34 J*s) * (3.00 x 10^8 m/s)]
N ≈ 2.05 x 10^22 photons
Therefore, approximately 2.05 x 10^22 photons are required to heat 1.25 g of water by 1.00°C, assuming all the photons are absorbed.
To calculate the number of photons required to heat 1.25 g of water by 1.00°C using microwave radiation, we need to follow these steps:
Step 1: Calculate the energy required to heat the water.
The energy required to heat a substance can be calculated using the formula:
Energy = (mass of the substance) * (specific heat capacity) * (change in temperature)
For water, the specific heat capacity is approximately 4.18 J/g°C.
First, convert the mass of water to kilograms:
1.25 g = 0.00125 kg
Next, calculate the energy required:
Energy = (0.00125 kg) * (4.18 J/g°C) * (1.00°C) = 0.005225 J
Step 2: Calculate the number of microwave photons.
The energy of a single photon can be determined using the formula:
Energy of a photon = (Planck's constant) * (speed of light) / (wavelength)
The speed of light is approximately 3.00 x 10^8 m/s, and the wavelength needs to be converted to meters:
12.2 cm = 0.122 m
The Planck's constant is approximately 6.63 x 10^-34 J·s.
Calculate the energy of a single photon:
Energy of a photon = (6.63 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (0.122 m) = 1.697 millionth Joules
Step 3: Calculate the number of photons required.
Number of photons = (Energy required) / (Energy of a photon)
Number of photons = 0.005225 J / (1.697 x 10^-6 J) ≈ 3079 photons
Therefore, approximately 3079 photons of microwave radiation with a wavelength of 12.2 cm are required to heat 1.25 g of water by 1.00°C, assuming all the photons are absorbed.