Question

The microwave radiation is absorbed by moisture in the food. it becomes hot, so does the rest of the food. How many photons having a wavelength of 3.00 mm would have to be absorbed by 1.00 g of water to raise its temperature by 1.00∘C?

Answer 1

To calculate the number of photons required to raise the temperature of 1.00 g of water by 1.00°C, we can use the following steps:

1. Calculate the energy required to raise the temperature of 1.00 g of water by 1.00°C.
2. Determine the energy of a single photon with a wavelength of 3.00 mm.
3. Divide the energy required for heating the water by the energy of a single photon to find the number of photons.

Step 1: Calculate the energy required to raise the temperature of 1.00 g of water by 1.00°C. The specific heat capacity of water is approximately 4.18 J/g°C. This means it takes 4.18 joules of energy to raise the temperature of 1 gram of water by 1°C.

Energy required = 4.18 J/g°C × 1.00 g × 1.00°C = 4.18 J

Step 2: Determine the energy of a single photon with a wavelength of 3.00 mm. The energy of a photon can be calculated using the formula:

Energy of a photon = h * c / λ

where: h = Planck's constant ≈ 6.626 x 10^-34 J·s c = speed of light ≈ 3.00 x 10^8 m/s (since the speed of light is given in m/s, we need to convert the wavelength to meters) λ = wavelength of the photon in meters

Let's convert the wavelength from mm to meters: Wavelength (λ) = 3.00 mm = 3.00 x 10^-3 m

Now, calculate the energy of a photon:

Energy of a photon = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (3.00 x 10^-3 m) Energy of a photon ≈ 6.626 x 10^-19 J

Step 3: Divide the energy required for heating the water by the energy of a single photon to find the number of photons:

Number of photons = Energy required / Energy of a photon Number of photons ≈ 4.18 J / (6.626 x 10^-19 J) ≈ 6.31 x 10^18 photons

So, approximately 6.31 x 10^18 photons with a wavelength of 3.00 mm would have to be absorbed by 1.00 g of water to raise its temperature by 1.00°C.