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. $$ \left(1 \mathrm{~nm}=10^{-9} \mathrm{~m}\right) $$. 5.3. The bowl of soup is now placed in a microwave oven of shorter wavelengths. How will the energy gained by the soup compare with the energy in 6.2 ? Write only DECREASES, REMAINS THE SAME, or INCREASES.

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6.2. The energy E of a photon is given by E = (h · c) / λ.

• h (Planck’s constant) = 6.626 × 10⁻³⁴ J·s  
• c (speed of light) = 3.0 × 10⁸ m/s  
• Given λ = 0.015 nm = 0.015 × 10⁻⁹ m = 1.5 × 10⁻¹¹ m

Calculating:
  E = (6.626 × 10⁻³⁴ J·s × 3.0 × 10⁸ m/s) / (1.5 × 10⁻¹¹ m)
   = (1.9878 × 10⁻²⁵ J·m) / (1.5 × 10⁻¹¹ m)
   ≈ 1.325 × 10⁻¹⁴ J

5.3. Since energy is inversely proportional to wavelength, using a shorter wavelength means each photon has higher energy. Thus, the energy gained by the soup, when subjected to microwaves of a shorter wavelength, INCREASES.
6.2. The energy of the microwave photons is approximately $$ 1.325 	imes 10^{-14} $$ joules. 5.3. The energy gained by the soup INCREASES when using shorter wavelength microwaves.

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