Question

q13. (3 points) sodium vapor street - lamps are well - known for their yellow - orange illumination because of photons with a frequency near 5.08×10^14 hz. find the wavelength (λ) of the radiation in meters, then convert λ to nanometers: v = s^(-1). so λ = = m or λ = = nm

Explanation:

Step1: Recall the speed - of - light formula

The speed of light $c$ is related to frequency $
u$ and wavelength $\lambda$ by the formula $c = \lambda
u$, where $c=3\times 10^{8}\ m/s$ and $
u = 5.08\times 10^{14}\ Hz = 5.08\times 10^{14}\ s^{-1}$. We can solve for $\lambda$: $\lambda=\frac{c}{
u}$.

Step2: Calculate the wavelength in meters

Substitute $c = 3\times 10^{8}\ m/s$ and $
u = 5.08\times 10^{14}\ s^{-1}$ into the formula $\lambda=\frac{c}{
u}$.
$\lambda=\frac{3\times 10^{8}\ m/s}{5.08\times 10^{14}\ s^{-1}}\approx5.91\times 10^{-7}\ m$.

Step3: Convert the wavelength from meters to nanometers

Since $1\ nm = 10^{-9}\ m$, to convert $\lambda$ from meters to nanometers, we use the conversion factor. $\lambda=(5.91\times 10^{-7}\ m)\times\frac{1\ nm}{10^{-9}\ m}= 591\ nm$.

Answer:

$
u = 5.08\times 10^{14}\ s^{-1}$
So $\lambda=\frac{3\times 10^{8}}{5.08\times 10^{14}}\approx5.91\times 10^{-7}\ m$
Or $\lambda = 591\ nm$