Question

calculate the wavelength of light with a frequency of 4.78 x 10^7 hz. answer: check

Explanation:

Step1: Recall the formula

The formula relating the speed of light ($c$), frequency ($
u$), and wavelength ($\lambda$) is $c = \lambda
u$. The speed of light $c = 3\times10^{8}\text{ m/s}$.

Step2: Rearrange the formula to solve for wavelength

We can rewrite the formula as $\lambda=\frac{c}{
u}$.

Step3: Substitute the values

Substitute $c = 3\times10^{8}\text{ m/s}$ and $
u = 4.78\times 10^{7}\text{ Hz}$ (since $1\text{ Hz}=1\text{ s}^{-1}$) into the formula:
$$\lambda=\frac{3\times 10^{8}\text{ m/s}}{4.78\times 10^{7}\text{ s}^{-1}}$$

Step4: Calculate the value

When we divide $3\times 10^{8}$ by $4.78\times 10^{7}$, we use the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. Here $a = 3$, $b=4.78$, $m = 8$, $n = 7$.
$$\lambda=\frac{3}{4.78}\times10^{8 - 7}\text{ m}$$
$$\lambda\approx0.628\times10^{1}\text{ m}$$
$$\lambda = 6.28\text{ m}$$

Answer:

$6.28\text{ m}$