Question

what is the wavelength of a yellow light with a frequency of 5.2 x 10^14 hz? give your answer in proper scientific notation. ? x 10^? m c = 3.0 x 10^8 m/s enter the coefficient in the green box and the exponent in the yellow box. coefficient (green) exponent (yellow) submit

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave 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 re - arrange the formula to $\lambda=\frac{c}{
u}$.

Step2: Substitute the given values

We know that $c = 3.0\times10^{8}\text{ m/s}$ and $
u = 5.2\times10^{14}\text{ Hz}$. Substituting these values into the formula $\lambda=\frac{c}{
u}$, we get $\lambda=\frac{3.0\times 10^{8}}{5.2\times 10^{14}}$.

Step3: Use the rule of exponents for division

When dividing numbers in scientific notation $a\times10^{m}$ by $b\times10^{n}$, we use the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $a = 3.0$, $b = 5.2$, $m = 8$, and $n = 14$. So $\frac{3.0}{5.2}\times10^{8-14}\approx0.577\times10^{- 6}$.

Step4: Convert to proper scientific notation

Proper scientific notation has a coefficient between 1 and 10. We can rewrite $0.577\times10^{-6}$ as $5.77\times10^{-7}$.

Answer:

Coefficient (green): $5.77$
Exponent (yellow): $-7$