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 $c = 3.00 \times 10^8$ m/s (speed of electromagnetic waves in vacuum). Rearrange to solve for wavelength: $\lambda = \frac{c}{f}$

Step2: Substitute given values

Substitute $c = 3.00 \times 10^8$ m/s and $f = 3.50 \times 10^{20}$ Hz into the formula:
$\lambda = \frac{3.00 \times 10^8}{3.50 \times 10^{20}}$

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: $\lambda \approx 0.857 \times 10^{-12}$ m, which can be written as $8.57 \times 10^{-13}$ m

Answer:

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