Question

Calculate the wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule. The $Cl—Cl$ bond energy is $243kJmo{l}^{-1}(h=6.6\times 10^{-34}Js;c=3\times 10^{8}m{s}^{-1}$, Avogadro’s number = $6.02\times 10^{-23}mol{e}^{-1}$)

• A. $4.91\times 10^{-7}M$
• B. $4.11\times 10^{-6}m$
• C. $8.81\times 10^{-31}m$
• D. $6.26\times 10^{-21}m$

Answer 1

Answer: (A)

Energy required to break one $Cl-Cl$ bond
$=\frac{\text{ Bond energy per mole }}{\text{ Avogadro’s number }}$
$=\frac{243\times 10^3}{6.023\times 10^{23}}J$
Let the wavelength of the photon required to break one $Cl-Cl$ bond be $\lambda$
$\lambda =\frac{hc}{E}=\frac{6.6\times 10^{-34}\times 3\times 10^8\times 6.023\times 10^{2.3}}{243\times 10^3}$
$=\frac{119.255\times 10^{-34}\times 10^{31}\times 10^{-3}}{243}$
$=4.91\times 10^{-7}m$