Question

what is the wavelength of a photon of light (in nm) whose frequency is 6.36 x 10^14 hz? answer:

Explanation:

Step1: Recall the formula

The relationship between the speed of light ($c$), wavelength ($\lambda$), and frequency ($
u$) 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 = 6.36\times 10^{14}\text{ Hz}$ and $c = 3\times10^{8}\text{ m/s}$.
$\lambda=\frac{3\times 10^{8}}{6.36\times 10^{14}}\text{ m}$.

Step4: Calculate the value

$\lambda=\frac{3}{6.36}\times10^{-6}\text{ m}\approx0.472\times 10^{-6}\text{ m}$.

Step5: Convert meters to nanometers

Since $1\text{ m}=10^{9}\text{ nm}$, so $\lambda = 0.472\times10^{-6}\times10^{9}\text{ nm}$.
$\lambda = 472\text{ nm}$.

Answer:

$472$