Question

calculate the energy for 1 mol of photons (an einstein) for light absorbed at 7.00×10² nm.
e = j

Explanation:

Step1: Convert wavelength to meters

Given $\lambda=7.00\times 10^{2}\text{ nm}=7.00\times 10^{2}\times 10^{-9}\text{ m}=7.00\times 10^{-7}\text{ m}$

Step2: Use the formula $E = h

u$ and $
u=\frac{c}{\lambda}$
The energy of one photon is $E_{photon}=h\frac{c}{\lambda}$, where $h = 6.626\times 10^{-34}\text{ Js}$ (Planck's constant) and $c = 3\times 10^{8}\text{ m/s}$ (speed of light).
Substitute the values:
$E_{photon}=\frac{6.626\times 10^{-34}\text{ Js}\times3\times 10^{8}\text{ m/s}}{7.00\times 10^{-7}\text{ m}}$
$E_{photon}=\frac{19.878\times 10^{-26}}{7.00\times 10^{-7}}\text{ J}$
$E_{photon}\approx 2.84\times 10^{-19}\text{ J}$

Step3: Calculate energy for 1 mole of photons

Using Avogadro's number $N_{A}=6.022\times 10^{23}\text{ mol}^{-1}$
$E = N_{A}\times E_{photon}$
$E=6.022\times 10^{23}\text{ mol}^{-1}\times2.84\times 10^{-19}\text{ J}$
$E = 6.022\times2.84\times 10^{4}\text{ J}$
$E\approx1.71\times 10^{5}\text{ J}$

Answer:

$1.71\times 10^{5}$