Question

what is the wavelength of a uv light with a frequency of 2.3×10^15 hz? give your answer in proper scientific notation.
?×10^? m
c = 3.0×10^8 m/s
enter the coefficient in the green box and the exponent in the yellow box.

Explanation:

Step1: Recall 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 want to solve for $\lambda$, so we can rewrite the formula as $\lambda=\frac{c}{
u}$.

Step2: Substitute the given values

We are given that $c = 3.0\times10^{8}\text{ m/s}$ and $
u=2.3\times 10^{15}\text{ Hz}$. Substituting these values into the formula $\lambda=\frac{c}{
u}$, we get $\lambda=\frac{3.0\times 10^{8}}{2.3\times 10^{15}}$.

Step3: Use the rules of exponents for division

When dividing numbers in scientific notation $a\times10^{m}$ by $b\times10^{n}$, we use the rule $\frac{a\times 10^{m}}{b\times 10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 3.0$, $b = 2.3$, $m = 8$, and $n = 15$. So $\frac{3.0}{2.3}\times10^{8-15}\approx1.3\times10^{-7}\text{ m}$.

Answer:

Coefficient (green): $1.3$
Exponent (yellow): $- 7$