Question

a photon of blue light has a frequency of 6.50×10¹⁴ hz. calculate the wavelength of this photon (c = 3.00×10⁸ m/s) in nanometers.

Explanation:

Step1: Recall the wave - speed formula

The formula relating the speed of light ($c$), frequency ($
u$), and wavelength ($\lambda$) is $c =
u\lambda$. We need to solve for $\lambda$, so $\lambda=\frac{c}{
u}$.

Step2: Substitute the given values

Given $c = 3.00\times 10^{8}\text{ m/s}$ and $
u=6.50\times 10^{14}\text{ Hz}$, then $\lambda=\frac{3.00\times 10^{8}\text{ m/s}}{6.50\times 10^{14}\text{ Hz}}$.

Step3: Calculate the wavelength in meters

$\lambda=\frac{3.00\times 10^{8}}{6.50\times 10^{14}}\text{ m}\approx4.62\times 10^{-7}\text{ m}$.

Step4: Convert meters to nanometers

Since $1\text{ m}=10^{9}\text{ nm}$, then $\lambda = 4.62\times 10^{-7}\text{ m}\times10^{9}\text{ nm/m}=462\text{ nm}$.

Answer:

462