an ultraviolet wave traveling through a vacuum has a wavelength of 4.0×10⁻⁷ m. the waves frequency, written…

Explanation:

Step1: Recall the wave - speed formula

The speed of light in a vacuum $c = 3\times10^{8}\ m/s$, and the wave - speed formula is $c=\lambda f$, where $c$ is the speed of the wave, $\lambda$ is the wavelength, and $f$ is the frequency. We need to solve for $f$, so $f=\frac{c}{\lambda}$.

Step2: Substitute the given values

Given $\lambda = 4.0\times 10^{-7}\ m$ and $c = 3\times10^{8}\ m/s$. Then $f=\frac{3\times 10^{8}}{4.0\times 10^{-7}}$. Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $f=\frac{3}{4.0}\times10^{8-(-7)}=\frac{3}{4.0}\times10^{15}$.

Step3: Calculate the coefficient

$\frac{3}{4.0}=0.75$. So $f = 0.75\times10^{15}\ Hz$. In scientific notation with two significant figures, we rewrite it as $f = 7.5\times10^{14}\ Hz$.

Answer:

$7.5$