Question

ch9. q1
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: Recall the formula

The formula for the speed of light is \(c = \lambda f\), where \(c\) is the speed of light (\(c = 3.00\times10^{8}\ m/s\)), \(\lambda\) is the wavelength, and \(f\) is the frequency. We need to solve for \(\lambda\), so \(\lambda=\frac{c}{f}\).

Step2: Substitute the values

Given \(c = 3.00\times10^{8}\ m/s\) and \(f = 2.73\times 10^{20}\ Hz\). Substitute these values into the formula: \(\lambda=\frac{3.00\times 10^{8}}{2.73\times 10^{20}}\).

Step3: Calculate the result

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

Answer:

The wavelength of the gamma - ray electromagnetic radiation is approximately \(1.10\times 10^{-12}\ m\).