green light has a wavelength of about 510 nm and travels at a speed of 3.00×10^8 m/s. the frequency of green…

green light has a wavelength of about 510 nm and travels at a speed of 3.00×10^8 m/s. the frequency of green light, rounded to the nearest tenth and written in scientific notation, is ×10^14 hz.

green light has a wavelength of about 510 nm and travels at a speed of 3.00×10^8 m/s. the frequency of green light, rounded to the nearest tenth and written in scientific notation, is ×10^14 hz.

Answer

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. We want to find $f$, so we can re - arrange the formula to $f=\frac{v}{\lambda}$.

Step2: Convert the wavelength to SI units

The wavelength $\lambda = 510\ nm=510\times10^{-9}\ m = 5.1\times10^{-7}\ m$. The speed of light $v = 3.00\times10^{8}\ m/s$.

Step3: Calculate the frequency

Substitute the values of $v$ and $\lambda$ into the formula $f=\frac{v}{\lambda}$. So $f=\frac{3.00\times 10^{8}}{5.1\times10^{-7}}$. Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $f=\frac{3.00}{5.1}\times10^{8-\left(-7\right)}=\frac{3.00}{5.1}\times10^{15}$. $\frac{3.00}{5.1}\approx0.588$, and $0.588\times10^{15}=5.9\times10^{14}\ Hz$ (rounded to the nearest tenth).

Answer:

$5.9$