Question

review:

1. calculate the energy of a light with a wavelength of 450 nm

step 1: convert wavelength (λ) from nm to m
step 2: use wavelength to calculate frequency (v)
v=(3.0×10⁸)÷(λ)

Explanation:

Step1: Convert wavelength ($\lambda$) from nm to m

Given $\lambda = 450\ nm$. Since $1\ nm=1\times10^{-9}\ m$, then $\lambda = 450\times10^{-9}\ m = 4.5\times 10^{-7}\ m$.

Step2: Use wavelength to calculate frequency ($

u$)
Using the formula $
u=\frac{c}{\lambda}$ where $c = 3.0\times10^{8}\ m/s$ and $\lambda=4.5\times 10^{-7}\ m$.
So, $
u=\frac{3.0\times 10^{8}}{4.5\times 10^{-7}}=\frac{3.0}{4.5}\times10^{8 + 7}=\frac{2}{3}\times10^{15}\ Hz\approx6.67\times 10^{14}\ Hz$.

Step3: Calculate the energy ($E$) of the light

Using the formula $E = h
u$ where $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant) and $
u\approx6.67\times 10^{14}\ Hz$.
$E=(6.626\times 10^{-34})\times(6.67\times 10^{14})$.
$E = 6.626\times6.67\times10^{-34 + 14}$.
$E\approx4.42\times 10^{-19}\ J$.

Answer:

The energy of the light is approximately $4.42\times 10^{-19}\ J$.