Question

1. calculate heating 235 g of water from 22.6°c to 94.4°c in a microwave oven requires 7.06 × 10⁴j of energy. if the microwave frequency is 2.88 × 10¹⁰ s⁻¹, how many quanta are required to supply the 7.06 × 10⁴ j?

Explanation:

Step1: Calculate energy of one quantum

Use Planck's equation \(E = h
u\), where \(h = 6.626\times10^{-34}\space J\cdot s\) (Planck's constant) and \(
u=2.88\times 10^{10}\space s^{-1}\) (frequency).
\(E=(6.626\times 10^{-34}\space J\cdot s)\times(2.88\times 10^{10}\space s^{-1})\)
\(E = 1.908\times10^{-23}\space J\)

Step2: Calculate number of quanta

Let \(n\) be the number of quanta. We know that the total energy \(E_{total}=7.06\times 10^{4}\space J\). Using the formula \(n=\frac{E_{total}}{E}\)
\(n=\frac{7.06\times 10^{4}\space J}{1.908\times 10^{-23}\space J}\)
\(n = 3.70\times10^{27}\)

Answer:

\(3.70\times 10^{27}\)