Question

what is the energy of a microwave photon that has a frequency of 1.12×10¹² hz? (h = 6.63×10⁻³⁴ js)

Explanation:

Step1: Recall the formula for photon energy

The energy of a photon is given by \(E = h
u\), where \(h\) is Planck's constant (\(h = 6.63\times10^{-34}\space Js\)) and \(
u\) is the frequency of the photon.

Step2: Substitute the given values into the formula

We are given \(h = 6.63\times 10^{-34}\space Js\) and \(
u=1.12\times 10^{12}\space Hz\). Substituting these values into the formula \(E = h
u\), we get \(E=(6.63\times 10^{-34})\times(1.12\times 10^{12})\).
Using the rule of exponents \(a^m\times a^n=a^{m + n}\), we have \(E=(6.63\times1.12)\times10^{-34 + 12}\).
First, calculate \(6.63\times1.12 = 7.4256\). Then, \(10^{-34+12}=10^{-22}\). So \(E = 7.4256\times10^{-22}\space J\).

Answer:

\(7.43\times 10^{-22}\space J\) (rounded to three significant figures)