Respuesta :
ANSWER
[tex]The\text{ wavelength of the radiation = 8.57 }\cdot10^{-3}m[/tex]STEP-BY-STEP EXPLANATION:
What to find? The wavelength of the electromagnetic radiation.
Given parameters
Frequency of the electromagnetic radiation = 3.5 * 10^10Hz
To find the wavelength of the electromagnetic radiation, we need to apply the below formula
[tex]\begin{gathered} C\text{ = f }\cdot\text{ }\lambda \\ \text{Where} \\ C\text{ = sp}eed\text{ of light} \\ f\text{ = frequency of the electromagnetic radiation} \\ \lambda\text{ = wavelength of the electromagnetic radiation} \end{gathered}[/tex]Note: The speed of light is given as 3 x 10^8 m/s
The next thing to do is to substitute the given parameters into the above formula
[tex]\begin{gathered} 3\cdot10^8\text{ = 3.5 }\cdot10^{10}\cdot\text{ }\lambda \\ \text{Divide both sides by 3.5 }\cdot10^{10} \\ \frac{3\cdot10^8}{3.5\cdot10^{10}}\text{ = }\frac{3.5\cdot10^{10}\lambda}{3.5\cdot10^{10}} \\ \lambda\text{ = }\frac{3\cdot10^8}{3.5\cdot10^{10}} \\ \lambda\text{ = }\frac{3}{3.5}\cdot10^{8\text{ - 10}} \\ \lambda\text{ = 0.857 }\cdot10^{-2} \\ \lambda\text{ = 8.57 }\cdot10^{-1}\cdot10^{-2} \\ \lambda\text{ = 8.57 }\cdot10^{-1-2} \\ \lambda\text{ = 8.57 }\cdot10^{-3}m \end{gathered}[/tex]