6.2. The wavelength of microwaves produced by a microwave oven machine is $$ 0,015 \mathrm{~nm} $$. A bowl of soup is placed inside the microwave oven. Calculate the energy of these microwave photons. $$ \left(1 \mathrm{~nm}=10^{-9} \mathrm{~m}\right) $$.

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UpStudy AI · Accepted Answer

We use the photon energy formula:

E = (h · c) / λ

where
  h = 6.63 × 10⁻³⁴ J·s (Planck’s constant),
  c = 3.0 × 10⁸ m/s (the speed of light),
  λ = 0.015 nm.

First, convert the wavelength to meters:

0.015 nm = 0.015 × 10⁻⁹ m = 1.5 × 10⁻¹¹ m.

Now substitute the values:

E = (6.63 × 10⁻³⁴ J·s × 3.0 × 10⁸ m/s) / (1.5 × 10⁻¹¹ m)

Multiply the numerator:

6.63 × 10⁻³⁴ × 3.0 × 10⁸ = 1.989 × 10⁻²⁵ J·m

Divide by the wavelength:

E = (1.989 × 10⁻²⁵ J·m) / (1.5 × 10⁻¹¹ m) ≈ 1.326 × 10⁻¹⁴ J

Thus, the energy of one photon is approximately 1.33 × 10⁻¹⁴ joules.

(Optional conversion to electronvolts, noting 1 eV = 1.602 × 10⁻¹⁹ J):

E ≈ (1.33 × 10⁻¹⁴ J) / (1.602 × 10⁻¹⁹ J/eV) ≈ 83,000 eV ≈ 83 keV

So the microwave photons have an energy of about 1.33 × 10⁻¹⁴ J (or roughly 83 keV) per photon.
The energy of each microwave photon is approximately 1.33 × 10⁻¹⁴ joules.

6.2. The wavelength of microwaves produced by a microwave oven machine is \( 0,015 \mathrm{~nm} \). A bowl of soup is placed inside the microwave oven. Calculate the energy of these microwave photons. \( \left(1 \mathrm{~nm}=10^{-9} \mathrm{~m}\right) \).

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