Question

calculate the frequency in hertz of electromagnetic radiation that has a wavelength of 546.0 nm. (c = 3.00×10^8 m/s)

Explanation:

Step1: Convert wavelength to meters

We know that $1\ nm = 10^{-9}\ m$. So, $\lambda=546.0\ nm = 546.0\times10^{-9}\ m$.

Step2: Use the wave - speed formula

The wave - speed formula is $c = \lambda
u$, where $c$ is the speed of light, $\lambda$ is the wavelength and $
u$ is the frequency. We can solve for $
u$: $
u=\frac{c}{\lambda}$.
Substitute $c = 3.00\times10^{8}\ m/s$ and $\lambda = 546.0\times10^{-9}\ m$ into the formula:
$
u=\frac{3.00\times 10^{8}\ m/s}{546.0\times10^{-9}\ m}$.

Step3: Calculate the frequency

$
u=\frac{3.00\times 10^{8}}{546.0\times10^{-9}}\ s^{-1}\approx5.49\times 10^{14}\ s^{-1}$.

Answer:

$5.49\times 10^{14}$