Question

what is the energy (in j) of a mole of photons that have a wavelength of 565 nm? (h = 6.626×10⁻³⁴ j·s and c = 3.00×10⁸ m/s)

Explanation:

Step1: Convert wavelength to meters

First, convert 565 nm to m. Since 1 nm = 10^(-9) m, so $\lambda=565\times10^{-9}\text{ m}$.

Step2: Calculate the energy of a single - photon

Use the formula $E = h
u$, and since $
u=\frac{c}{\lambda}$, then $E=\frac{hc}{\lambda}$. Substitute $h = 6.626\times10^{-34}\text{ J}\cdot\text{s}$, $c = 3.00\times10^{8}\text{ m/s}$ and $\lambda = 565\times10^{-9}\text{ m}$ into the formula:
$E=\frac{6.626\times 10^{-34}\text{ J}\cdot\text{s}\times3.00\times 10^{8}\text{ m/s}}{565\times10^{-9}\text{ m}}\approx3.52\times10^{-19}\text{ J}$

Step3: Calculate the energy of a mole of photons

Use Avogadro's number $N_A = 6.022\times10^{23}\text{ mol}^{-1}$. The energy of a mole of photons $E_{mol}=N_A\times E$.
$E_{mol}=6.022\times 10^{23}\text{ mol}^{-1}\times3.52\times10^{-19}\text{ J}\approx2.12\times10^{5}\text{ J/mol}$

Answer:

$2.12\times 10^{5}$