Question

what is the energy (in j) of a mole of photons that have a wavelength of 555 nm? (h = 6.626×10⁻³⁴ j·s and c = 3.00×10⁸ m/s)

Explanation:

Step1: Convert wavelength to meters

The wavelength $\lambda = 555\ nm=555\times10^{- 9}\ m$.

Step2: Calculate the energy of a single - photon

The energy of a photon is given by the formula $E = h
u$, and since $
u=\frac{c}{\lambda}$, then $E=\frac{hc}{\lambda}$. Substitute $h = 6.626\times10^{-34}\ J\cdot s$, $c = 3.00\times10^{8}\ m/s$ and $\lambda=555\times10^{-9}\ m$ into the formula:
$E=\frac{6.626\times10^{-34}\ J\cdot s\times3.00\times10^{8}\ m/s}{555\times10^{-9}\ m}\approx3.58\times10^{-19}\ J$.

Step3: Calculate the energy of a mole of photons

One mole of photons contains $N_A = 6.022\times10^{23}$ photons. The energy of a mole of photons $E_{mol}=N_A\times E$.
$E_{mol}=6.022\times10^{23}\times3.58\times10^{-19}\ J\approx2.15\times10^{5}\ J$.

Answer:

$2.15\times 10^{5}$