Question

it takes 614 kj/mol to break a carbon - carbon double bond. calculate the maximum wavelength of light for which a carbon - carbon double bond could be broken by absorbing a single photon. round your answer to 3 significant digits.

Explanation:

Step1: Convert energy per mole to energy per photon

First, convert the energy required to break a carbon - carbon double bond from kJ/mol to J/photon. We know that 1 mole = $6.022\times 10^{23}$ photons and 1 kJ = 1000 J.
$E=\frac{614\times1000\ J/mol}{6.022\times 10^{23}\ photons/mol}\approx1.02\times 10^{-18}\ J/photon$

Step2: Use the energy - wavelength relationship

The energy of a photon is given by the formula $E = h
u=\frac{hc}{\lambda}$, where $h = 6.626\times 10^{-34}\ J\cdot s$ (Planck's constant), $c= 2.998\times 10^{8}\ m/s$ (speed of light), and $\lambda$ is the wavelength.
We can re - arrange the formula to solve for $\lambda$: $\lambda=\frac{hc}{E}$.
Substitute $h = 6.626\times 10^{-34}\ J\cdot s$, $c = 2.998\times 10^{8}\ m/s$ and $E = 1.02\times 10^{-18}\ J$ into the formula.
$\lambda=\frac{6.626\times 10^{-34}\ J\cdot s\times2.998\times 10^{8}\ m/s}{1.02\times 10^{-18}\ J}\approx1.95\times 10^{-7}\ m$

Step3: Convert to nanometers

Since 1 m = $10^{9}$ nm, then $\lambda=1.95\times 10^{-7}\ m\times10^{9}\ nm/m = 195\ nm$

Answer:

195 nm