Question
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.
Ask by Gray Carlson. in South Africa
Feb 26,2025
Upstudy AI Solution
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Answer
6.2. The energy of the microwave photons is approximately \( 1.325 \times 10^{-14} \) joules.
5.3. The energy gained by the soup INCREASES when using shorter wavelength microwaves.
Solution
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.
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The energy of the microwave photons can be calculated using the formula \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \mathrm{~Js} \)), \( c \) is the speed of light (\( 3 \times 10^8 \mathrm{~m/s} \)), and \( \lambda \) is the wavelength in meters. To convert 0.015 nm to meters, you multiply it by \( 10^{-9} \) to get \( 0.015 \times 10^{-9} \mathrm{~m} \) or \( 1.5 \times 10^{-11} \mathrm{~m} \). Plugging these values into the formula gives the energy of those microwave photons. For the second part, since shorter wavelengths correspond to higher energy photons, the energy gained by the soup will INCREASES.
