Question

question 15 of 30
what is the wavelength of an electromagnetic wave that has a frequency of
7.80 × 10¹⁴ hz in a vacuum? (the speed of light in a vacuum is 3.00 × 10⁸
m/s.)

a. 2.34 × 10²³ m
b. 2.60 × 10⁶ m
c. 3.85 × 10⁻⁷ m
d. 1.28 × 10⁻¹⁵ m

Explanation:

Step1: Recall the wave - speed formula

The formula that relates the speed of a wave (\(v\)), its wavelength (\(\lambda\)) and its frequency (\(f\)) is \(v = \lambda f\). We can rearrange this formula to solve for the wavelength: \(\lambda=\frac{v}{f}\).

Step2: Identify the given values

We are given that the speed of light in a vacuum \(v = 3.00\times10^{8}\space m/s\) and the frequency of the electromagnetic wave \(f = 7.80\times10^{14}\space Hz\) (since \(Hz=\frac{1}{s}\)).

Step3: Substitute the values into the formula

Substitute \(v = 3.00\times10^{8}\space m/s\) and \(f = 7.80\times10^{14}\space Hz\) into the formula \(\lambda=\frac{v}{f}\):
\[

$$\begin{align*} \lambda&=\frac{3.00\times 10^{8}\space m/s}{7.80\times 10^{14}\space Hz}\\ &=\frac{3.00}{7.80}\times\frac{10^{8}}{10^{14}}\space m\\ &= 0.3846\times10^{- 6}\space m\\ &=3.85\times 10^{-7}\space m \end{align*}$$

\]

Answer:

C. \(3.85\times 10^{-7}\space m\)