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Chapter 6: Q6.2CYL (page 299)

The microwaves in an oven are of a specific frequency that will heat the water molecules contained in food.(This is why most plastics and glass do not become hot in a microwave oven-they do not contain watermolecules.) This frequency is about\({\bf{3}} \times {\bf{1}}{{\bf{0}}^{\bf{9}}}{\rm{ }}{\bf{Hz}}\). What is the energy of one photon in these microwaves?

Short Answer

Expert verified

The energy of one photon in these microwaves is \(2.08{\rm{ }} \times {\rm{ }}{10^{ - 24}}J\)

Step by step solution

01

Determination of wavelength of the radiation

\(\begin{aligned}{}C = v\lambda \\\lambda = c/v\\ = (2.998 \times {10^8}m{s^{ - 1}})/(3 \times {10^9}{s^{ - 1}})?\\ = 0.99 \times {10^{ - 1}}m\\ = 0.099m\end{aligned}\)

02

Energy of the radiation

\(\begin{aligned}E = hc/\lambda \ &\ = (2.998 \times {10^8}m{s^{ - 1}} \times 6.626 \times {10^{ - 34}})/(0.09m)\\ = 208.6 \times {10^{ - 26}}J\end{aligned}\)

Hence, the energy of one photon in these microwaves is\({\bf{2}}.{\bf{08}}{\rm{ }} \times {\rm{ }}{\bf{1}}{{\bf{0}}^{ - {\bf{24}}}}{\bf{J}}\).

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