Question

what is the wavelength of a yellow light with a frequency of 5.2 x 10¹⁴ hz? give your answer in proper scientific notation.
? x 10^? m
c = 3.0 x 10⁸ m/s
enter the coefficient in the green box and the exponent in the yellow box.
coefficient (green)
exponent (yellow)

Explanation:

Step1: Recall the formula

The formula relating the speed of light ($c$), frequency ($f$), and wavelength ($\lambda$) is $c = f\lambda$. We can rearrange it to find $\lambda=\frac{c}{f}$.

Step2: Substitute the values

Given $c = 3.0\times10^{8}\text{ m/s}$ and $f = 5.2\times10^{14}\text{ Hz}$. Then $\lambda=\frac{3.0\times 10^{8}}{5.2\times 10^{14}}$.
Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{3.0}{5.2}\times10^{8-14}$.
$\frac{3.0}{5.2}\approx0.577$ and $10^{8 - 14}=10^{-6}$.
$0.577\times10^{-6}=5.77\times10^{-7}$ (in proper scientific notation, the coefficient should be between 1 and 10).

Answer:

Coefficient (green): $5.8$ (rounded to one decimal place)
Exponent (yellow): $-7$