Question

question 25 of 33
an x - ray with a wavelength of 3.5×10^(-9) m travels with a speed of 3.0×10^8 m/s. what is the frequency of this electromagnetic wave?
a. 8.57×10^16 hz
b. 1.05 hz
c. 9.52×10^(-1) hz
d. 1.17×10^(-17) hz

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. We need to solve for $f$, so we can rewrite the formula as $f=\frac{v}{\lambda}$.

Step2: Substitute the given values

We are given that $v = 3.0\times10^{8}\text{ m/s}$ and $\lambda=3.5\times 10^{-9}\text{ m}$. Substituting these values into the formula $f=\frac{v}{\lambda}$, we get $f=\frac{3.0\times 10^{8}}{3.5\times 10^{-9}}$.

Step3: Perform the calculation

Using the rules of exponents for division ($\frac{a^{m}}{a^{n}}=a^{m - n}$), we have $f=\frac{3.0}{3.5}\times10^{8-(- 9)}=\frac{3.0}{3.5}\times10^{17}$. $\frac{3.0}{3.5}\approx0.857$, so $f = 0.857\times10^{17}=8.57\times 10^{16}\text{ Hz}$.

Answer:

A. $8.57\times 10^{16}\text{ Hz}$