what is the frequency of light having a wavelength of 876 nm? what is the wavelength (in nm) of radiation…

Explanation:

Step1: Recall the speed - of - light formula

The speed of light $c=\lambda\nu$, where $c = 3.00\times10^{8}\ m/s$ (speed of light in a vacuum), $\lambda$ is the wavelength and $\nu$ is the frequency.

Step2: Solve for frequency in Part 1

Given $\lambda=876\ nm = 876\times10^{-9}\ m$. Rearranging the formula $\nu=\frac{c}{\lambda}$. Substitute $c = 3.00\times10^{8}\ m/s$ and $\lambda = 876\times10^{-9}\ m$ into the formula: $\nu=\frac{3.00\times10^{8}\ m/s}{876\times10^{-9}\ m}\approx3.43\times 10^{14}\ Hz$.

Step3: Solve for wavelength in Part 2

Given $\nu = 3.15\times10^{9}\ Hz$. Rearranging the formula $\lambda=\frac{c}{\nu}$. Substitute $c = 3.00\times10^{8}\ m/s$ and $\nu=3.15\times10^{9}\ Hz$ into the formula: $\lambda=\frac{3.00\times10^{8}\ m/s}{3.15\times10^{9}\ Hz}\approx0.0952\ m$. Convert to nm: $\lambda = 0.0952\ m\times10^{9}\ nm/m = 95.2\ nm$.

Answer:

Part 1 of 2: $3.43\times 10^{14}$ Hz Part 2 of 2: $95.2$ nm