Question

what is the frequency of a radar photon with energy 6.80×10^{-25} j? (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 \(E\) is the energy, \(h\) is Planck's constant, and \(
u\) is the frequency. We need to solve for \(
u\), so \(
u=\frac{E}{h}\).

Step2: Substitute the given values

We are given \(E = 6.80\times10^{-25}\text{ J}\) and \(h = 6.63\times10^{-34}\text{ J}\cdot\text{s}\). Substituting these into the formula: \(
u=\frac{6.80\times 10^{-25}\text{ J}}{6.63\times 10^{-34}\text{ J}\cdot\text{s}}\).

Step3: Calculate the frequency

When we divide \(6.80\times 10^{-25}\) by \(6.63\times 10^{-34}\), we use the rule \(\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}\). Here, \(\frac{6.80}{6.63}\approx1.03\) and \(m - n=- 25-(-34)=9\). So \(
u\approx1.03\times10^{9}\text{ Hz}\).

Answer:

\(1.03\times 10^{9}\text{ Hz}\)