Question

1. calculate the wavelength of light that has a frequency of 5.2×10¹⁴s⁻¹.

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 in a vacuum $c=3\times 10^{8}\ m/s$.

Step2: Rearrange the formula to solve for wavelength

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

Step3: Substitute the given values

Substitute $c = 3\times 10^{8}\ m/s$ and $
u=5.2\times 10^{14}\ s^{-1}$ into the formula:
$\lambda=\frac{3\times 10^{8}}{5.2\times 10^{14}}$

Step4: Perform the calculation

Using the rules of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\frac{3}{5.2}\times10^{8-14}$.
$\frac{3}{5.2}\approx0.577$, and $10^{8 - 14}=10^{-6}$.
So $\lambda\approx0.577\times 10^{- 6}\ m$.
Converting to nanometers (since $1\ m = 10^{9}\ nm$), $\lambda=0.577\times10^{-6}\times10^{9}\ nm = 577\ nm$.

Answer:

The wavelength of the light is approximately $577\ nm$.