Question

what is the energy of a microwave photon that has a frequency of 1.12×10^{12} hz? (h = 6.63×10^{-34} j·s)

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 and \(
u\) is the frequency.

Step2: Substitute the given values

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

Answer:

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