Question

practice problems: electromagnetic wave calculations

1. what does it mean if variables have an inverse relationship?
2. a laser emits light of frequency ( 5.00\times10^{14}sec^{-1}) (hz). what is the wavelength of the light? in nm (nanometers)?
3. a laser emits light of frequency ( 4.74\times10^{3}sec^{-1}) (hz). what is the energy of the wave?
4. an electromagnetic wave has a wavelength of ( 1.00\times10^{-8}) m, how much energy does this wave have?

Explanation:

Step1: Recall the formula for wavelength

The formula for the wavelength ($\lambda$) of an electromagnetic wave is $\lambda=\frac{c}{f}$, where $c = 3\times10^{8}\ m/s$ (speed of light) and $f$ is the frequency.

Step2: Substitute the given values

Given $f = 5.00\times10^{14}\ Hz$, we substitute into the formula:
$$\lambda=\frac{3\times10^{8}\ m/s}{5.00\times10^{14}\ Hz}$$
$$\lambda = 6\times10^{-7}\ m$$

Step3: Convert meters to nanometers

Since $1\ m=10^{9}\ nm$, we convert:
$$\lambda=6\times10^{-7}\times10^{9}\ nm$$
$$\lambda = 600\ nm$$

Answer:

The wavelength of the light is $600\ nm$.