Question

What is the wavelength with a frequency the frequency of 3.5 × 10^10 Hz?

Answer 1

`The\text{ wavelength of the radiation = 8.57 }\cdot10^(-3)m`

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

`\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}`

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

`\begin{gathered} 3\cdot10^8\text{ = 3.5 }\cdot10^(10)\cdot\text{ }\lambda \\ \text{Divide both sides by 3.5 }\cdot10^(10) \\ (3\cdot10^8)/(3.5\cdot10^(10))\text{ = }(3.5\cdot10^(10)\lambda)/(3.5\cdot10^(10)) \\ \lambda\text{ = }(3\cdot10^8)/(3.5\cdot10^(10)) \\ \lambda\text{ = }(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}`