To find the wavelength of an electromagnetic wave, you can use the formula:
[tex]\[ \lambda = \frac{v}{f} \][/tex]
where:
- [tex]\(\lambda\)[/tex] is the wavelength,
- [tex]\(v\)[/tex] is the speed of light, and
- [tex]\(f\)[/tex] is the frequency.
Given the values:
- The frequency [tex]\( f \)[/tex] is [tex]\( 4.0 \times 10^{18} \)[/tex] Hz.
- The speed of light [tex]\( v \)[/tex] is [tex]\( 3.0 \times 10^8 \)[/tex] m/s.
Substitute the given values into the formula:
[tex]\[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{4.0 \times 10^{18} \, \text{Hz}} \][/tex]
Now, perform the division:
[tex]\[ \lambda = \frac{3.0}{4.0} \times 10^{8} \times 10^{-18} \][/tex]
[tex]\[ \lambda = 0.75 \times 10^{-10} \][/tex]
Expressing it in scientific notation, we get:
[tex]\[ \lambda = 7.5 \times 10^{-11} \, \text{m} \][/tex]
So, the correct answer is:
B. [tex]\( 7.5 \times 10^{-11} \, \text{m} \)[/tex]
