Question

what is the frequency of a blue light with a wavelength of 4.83 x 10^-7 m? give your answer in proper scientific notation. ? x 10^? hz c = 3.0 x 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 need to solve for $
u$, so $
u=\frac{c}{\lambda}$.

Step2: Substitute the given values

We know that $c = 3.0\times10^{8}\text{ m/s}$ and $\lambda = 4.83\times10^{-7}\text{ m}$. Then $
u=\frac{3.0\times 10^{8}}{4.83\times 10^{-7}}$.

Step3: Use the rule of exponents for division

When dividing numbers in scientific notation $a\times10^{m}$ by $b\times10^{n}$, we use the formula $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here, $\frac{3.0}{4.83}\approx0.621$ and $m - n=8-(-7)=15$. So $
u = 0.621\times10^{15}\text{ Hz}$.

Step4: Convert to proper scientific notation

In proper scientific notation, the coefficient $a$ should be in the range $1\leq a<10$. So $0.621\times10^{15}=6.21\times10^{14}\text{ Hz}$.

Answer:

Coefficient (green): $6.21$
Exponent (yellow): $14$