Question

question 21 of 25
if an electromagnetic wave has a frequency of ( 8\times10^{14}\text{ hz} ), what is its wavelength? use ( lambda=\frac{v}{f} ). the speed of light is ( 3\times10^{8}\text{ m/s} ).
a. ( 2.7\times10^{6}\text{ m} )
b. ( 3.8\times10^{-7}\text{ m} )
c. ( 3.8\times10^{21}\text{ m} )
d. ( 2.7\times10^{6}\text{ m} )

Explanation:

Step1: Substitute the values into the formula

Given \(v = 3\times10^{8}\text{ m/s}\) and \(f=8\times 10^{14}\text{ Hz}\), substitute into \(\lambda=\frac{v}{f}\).
\(\lambda=\frac{3\times 10^{8}}{8\times 10^{14}}\)

Step2: Simplify the expression

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{3}{8}\times10^{8-14}\).
\(\frac{3}{8}=0.375\approx0.38\), and \(10^{8 - 14}=10^{-6}\).
So \(\lambda = 0.38\times10^{- 6}\text{ m}=3.8\times10^{-7}\text{ m}\)

Answer:

B. \(3.8\times 10^{-7}\text{ m}\)