Answered

An electromagnetic wave has a frequency of [tex]\(4.0 \times 10^{18} \, \text{Hz}\)[/tex]. What is the wavelength of the wave? Use the equation [tex]\(\lambda = \frac{v}{f}\)[/tex] and [tex]\(3.0 \times 10^8 \, \text{m/s}\)[/tex] for the speed of light.

A. [tex]\(7.5 \times 10^{-11} \, \text{m}\)[/tex]

B. [tex]\(1.3 \times 10^{10} \, \text{m}\)[/tex]

C. [tex]\(7.5 \times 10^{26} \, \text{m}\)[/tex]

D. [tex]\(1.3 \times 10^{-26} \, \text{m}\)[/tex]



Answer :

To determine the wavelength [tex]\(\lambda\)[/tex] of an electromagnetic wave, we can use the equation:

[tex]\[\lambda = \frac{v}{f}\][/tex]

where [tex]\( v \)[/tex] is the speed of light and [tex]\( f \)[/tex] is the frequency of the wave.

Given:
- Frequency, [tex]\( f = 4.0 \times 10^{18} \)[/tex] Hz
- Speed of light, [tex]\( v = 3.0 \times 10^8 \)[/tex] m/s

We can substitute these values into the equation to find the wavelength.

[tex]\[\lambda = \frac{v}{f} = \frac{3.0 \times 10^8 \, \text{m/s}}{4.0 \times 10^{18} \, \text{Hz}}\][/tex]

When we perform the division:

[tex]\[\lambda = 7.5 \times 10^{-11} \, \text{m}\][/tex]

Thus, the wavelength of the electromagnetic wave is [tex]\( 7.5 \times 10^{-11} \, \text{m} \)[/tex].

Therefore, the correct answer is:

A. [tex]\( 7.5 \times 10^{-11} \, \text{m} \)[/tex]