Question

what is the wavelength of gamma ray electromagnetic radiation with a frequency of 2.73×10²⁰ hz? (c = 3.00×10⁸ m/s)

Explanation:

Step1: Use the formula for the speed of light

The formula is \(c = \lambda
u\), where \(c\) is the speed of light (\(c = 3.00\times10^{8}\space m/s\)), \(\lambda\) is the wavelength, and \(
u\) is the frequency (\(
u=2.73\times 10^{20}\space Hz\)). We need to solve for \(\lambda\), so we can rewrite the formula as \(\lambda=\frac{c}{
u}\).

Step2: Substitute the values into the formula

Substitute \(c = 3.00\times10^{8}\space m/s\) and \(
u = 2.73\times10^{20}\space Hz\) into \(\lambda=\frac{c}{
u}\).

$$ \lambda=\frac{3.00\times 10^{8}}{2.73\times 10^{20}} $$

Step3: Calculate the value

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{3.00}{2.73}\times10^{8-20}\).
\(\frac{3.00}{2.73}\approx1.099\), and \(10^{8 - 20}=10^{- 12}\). So \(\lambda\approx1.10\times10^{-12}\space m\)

Answer:

\(1.10\times 10^{-12}\space m\)