To find the wavelength of an X-ray with a given frequency, we will use the formula that relates the speed of light ([tex]\( c \)[/tex]), the frequency ([tex]\( f \)[/tex]), and the wavelength ([tex]\( \lambda \)[/tex]):
[tex]\[ c = \lambda f \][/tex]
We need to solve for the wavelength ([tex]\( \lambda \)[/tex]):
[tex]\[ \lambda = \frac{c}{f} \][/tex]
Given:
- Speed of light, [tex]\( c = 3.00 \times 10^8 \)[/tex] meters per second
- Frequency, [tex]\( f = 1.18 \times 10^{18} \)[/tex] Hz
Let's plug these values into the formula:
[tex]\[ \lambda = \frac{3.00 \times 10^8 \text{ meters/second}}{1.18 \times 10^{18} \text{ Hz}} \][/tex]
Perform the division:
[tex]\[ \lambda = \frac{3.00}{1.18} \times \frac{10^8}{10^{18}} \][/tex]
[tex]\[ \lambda = 2.5423728813559323 \times 10^{-10} \text{ meters} \][/tex]
Now, we will match this value with the given options to find the correct answer. The calculated wavelength [tex]\(2.5423728813559323 \times 10^{-10} \text{ meters}\)[/tex] is very close to the provided option:
[tex]\[2.54 \times 10^{-10} \text{ meters}\][/tex]
Thus, the wavelength of the X-ray is:
[tex]\[2.54 \times 10^{-10} \text{ meters}\][/tex]
So, the correct answer is:
[tex]\[ \boxed{2.54 \times 10^{-10} \text{ meters}} \][/tex]
