Question

x-rays are often used as a diagnostic tool to measure bone tissue. the frequency of a particular x-ray device is 3.50 x 10²⁰ hz. what is the wavelength in meters? x 10^? m

Explanation:

Step1: Recall wave speed formula

The relationship between wave speed ($c$), frequency ($f$), and wavelength ($\lambda$) is $c = f\lambda$, where $c$ is the speed of light in vacuum, $c=3.00\times10^8\ \text{m/s}$. Rearrange to solve for wavelength:
$\lambda = \frac{c}{f}$

Step2: Substitute given values

Substitute $c=3.00\times10^8\ \text{m/s}$ and $f=3.50\times10^{20}\ \text{Hz}$:
$\lambda = \frac{3.00\times10^8}{3.50\times10^{20}}$

Step3: Calculate the result

First compute the coefficient: $\frac{3.00}{3.50} \approx 0.857$
Then compute the exponent: $10^{8-20}=10^{-12}$
Combine terms: $\lambda \approx 0.857\times10^{-12} = 8.57\times10^{-13}$

Answer:

$8.57 \times 10^{-13}$ m