Question

a dental hygienist uses x-rays (λ = 1.00 å) to take a series of dental radiographs while a patient listens to a radio station (λ = 325 cm). what is the frequency (in s⁻¹) of the electromagnetic radiation from each source?
useful information
1 å = 10⁻¹⁰ m
1 cm = 10⁻² m
ν = c/λ

Explanation:

Step1: Convert X - ray wavelength to meters

Given \(1\mathring{A}=10^{- 10}\space m\), and the X - ray wavelength \(\lambda_{x - ray}=1.00\mathring{A}\). So \(\lambda_{x - ray}=1.00\times10^{-10}\space m\). The speed of light \(c = 3.00\times10^{8}\space m/s\). Using the formula \(v=\frac{c}{\lambda}\), for X - rays:
\(v_{x - ray}=\frac{3.00\times10^{8}\space m/s}{1.00\times10^{-10}\space m}=3.00\times10^{18}\space s^{-1}\)

Step2: Convert radio wavelength to meters

Given \(1\space cm = 10^{-2}\space m\), and the radio wavelength \(\lambda_{radio}=325\space cm\). So \(\lambda_{radio}=325\times10^{-2}\space m = 3.25\space m\). Using the formula \(v=\frac{c}{\lambda}\), for radio waves:
\(v_{radio}=\frac{3.00\times10^{8}\space m/s}{3.25\space m}\approx9.23\times10^{7}\space s^{-1}\)

Answer:

• Frequency of X - rays: \(\boldsymbol{3.00\times10^{18}\space s^{-1}}\)
• Frequency of radio waves: \(\boldsymbol{\approx9.23\times10^{7}\space s^{-1}}\)