Question

what is the frequency of the radiation?
$lambda = 5.60 \times 10^{-13}$ 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 $c = 3.00 \times 10^8 \, \text{m/s}$. Rearrange to solve for frequency:

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

Step2: Substitute given values

Substitute $c = 3.00 \times 10^8 \, \text{m/s}$ and $\lambda = 5.60 \times 10^{-13} \, \text{m}$:

$$ u = \frac{3.00 \times 10^8}{5.60 \times 10^{-13}}$$

Step3: Calculate the value

Divide the coefficients and subtract exponents:

$$ u = \frac{3.00}{5.60} \times 10^{8 - (-13)} \approx 0.536 \times 10^{21} = 5.36 \times 10^{20}$$

Answer:

$5.36 \times 10^{20} \, \text{s}^{-1}$