Question

calculate the wavelength of light with a frequency of 5.42 x 10^{17} 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

$\lambda=\frac{c}{
u}$.

Step3: Substitute the values

Given $
u = 5.42\times 10^{17}\text{ Hz}$, substitute $c = 3\times10^{8}\text{ m/s}$ and $
u$ into the formula:
$\lambda=\frac{3\times 10^{8}}{5.42\times 10^{17}}$

Step4: Calculate the value

Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\lambda=\frac{3}{5.42}\times10^{8-17}$.
$\frac{3}{5.42}\approx0.5535$, and $10^{8 - 17}=10^{-9}$.
So $\lambda=0.5535\times10^{-9}\text{ m}=5.54\times 10^{-10}\text{ m}$ (rounded to three significant figures).

Answer:

$5.54\times 10^{-10}\text{ m}$