Microwave radiation is absorbed by the water in food. As the water absorbs the heat it causes the food to get hot. If the wavelength of a microwave is 10, calculate the frequency and the energy of each photon.

1) The frequency of each photon is 3.0 × 10⁹ Hz

2) The energy of each photon is 1.98786 × 10⁻²⁴ J

Explanation:

The energy, 'E', in a photon of light is given by Planck's equation as follows;

E = h·f = h·c/λ

Where;

E = The energy of a photon

h = Planck constant = 6.6262 × 10⁻³⁴ J·s

f = The frequency of the photon/radiation

c = The speed of light = 3.0 × 10⁸ m/s

λ = The wavelength of the photon/radiation

The given parameters of the microwave are;

The wavelength, λ = 10 cm = 0.1 m

The type of wave = Microwave

1) From E = h·f = h·c/λ, we find that the frequency, 'f' equals c/λ

∴ f = 3.0 × 10⁸ m/s/(0.1 m) = 3.0 × 10⁹ 1/s = 3.0 × 10⁹ Hz

The frequency of each photon, f = 3.0 × 10⁹ Hz

2) From E = h·f = h·c/λ, the energy, 'E', of each photon is given as follows;

E = h·c/λ = 6.6262 × 10⁻³⁴ J·s × 3.0 × 10⁸ m/s/(0.1 m) = 1.98786 × 10⁻²⁴ J

The energy of each photon, E = 1.98786 × 10⁻²⁴ J

8 m/s because for him to get the same amount of energy as ray is putting out, bobby, who weighs half as much as ray, needs to run twice as fast.