Question

frequency (s-1) | wavelength (nm)
| 123
2.34e14 |
7.85e19 |
| 790

Explanation:

Step1: Recall wave speed formula

The relationship between frequency ($
u$), wavelength ($\lambda$), and the speed of light ($c$) is $c =
u\lambda$, where $c = 3.00\times10^{8}\ \text{m/s}$. Rearrange to solve for unknowns:
$
u = \frac{c}{\lambda}$ or $\lambda = \frac{c}{
u}$
First, convert wavelength from nm to m: $1\ \text{nm}=10^{-9}\ \text{m}$

Step2: Calculate freq for 123 nm

Convert $\lambda=123\ \text{nm}=123\times10^{-9}\ \text{m}$
$
u = \frac{3.00\times10^{8}}{123\times10^{-9}} \approx 2.44\times10^{15}\ \text{s}^{-1}$

Step3: Calculate wavelength for 2.34E14 s⁻¹

$\lambda = \frac{3.00\times10^{8}}{2.34\times10^{14}} = 1.28\times10^{-6}\ \text{m} = 1280\ \text{nm}$

Step4: Calculate wavelength for 7.85E19 s⁻¹

$\lambda = \frac{3.00\times10^{8}}{7.85\times10^{19}} = 3.82\times10^{-12}\ \text{m} = 3.82\times10^{-3}\ \text{nm}$

Step5: Calculate freq for 790 nm

Convert $\lambda=790\ \text{nm}=790\times10^{-9}\ \text{m}$
$
u = \frac{3.00\times10^{8}}{790\times10^{-9}} \approx 3.80\times10^{14}\ \text{s}^{-1}$

Answer:

Frequency (s⁻¹)	Wavelength (nm)
$2.34\times10^{14}$	1280
$7.85\times10^{19}$	$3.82\times10^{-3}$
$3.80\times10^{14}$	790