Question

what is the frequency of the radiation?
$\lambda = 1.238 \times 10^{-2}$ m
$? \times 10^{?}$ $s^{-1}$

Explanation:

Step1: Recall wave speed formula

The relationship between the speed of electromagnetic radiation ($c$), wavelength ($\lambda$), and frequency ($
u$) is $c = \lambda
u$, where $c = 3.00 \times 10^8 \, \text{m/s}$. Rearranged to solve for frequency:
$
u = \frac{c}{\lambda}$

Step2: Substitute given values

Substitute $c = 3.00 \times 10^8 \, \text{m/s}$ and $\lambda = 1.238 \times 10^{-2} \, \text{m}$:
$
u = \frac{3.00 \times 10^8}{1.238 \times 10^{-2}}$

Step3: Calculate the result

First compute the numerical coefficient: $\frac{3.00}{1.238} \approx 2.423$
Then handle the exponents: $10^{8 - (-2)} = 10^{10}$
Combine to get: $
u \approx 2.423 \times 10^{10} \, \text{s}^{-1}$

Answer:

$2.42 \times 10^{10} \, \text{s}^{-1}$ (rounded to three significant figures)