Question

Calculate the wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule. The $\text{Cl-Cl}$ bonding energy is $243kJmo{{l}^{-1}}$.$(h=6.6\times {{10}^{-34}}Js;c=3\times {{10}^{8}}m{{s}^{-1}}$, Avogadro’s number$=6.023\times {{10}^{23}}mol{{e}^{-1}})$.
$4.91\times {{10}^{-7}}m$$4.11\times {{10}^{-6}}m$
$8.81\times {{10}^{-31}}m$
$6.26\times {{10}^{-21}}m$

Answer 1

Hint : In this question, we find the wavelength of light which is required to break the two chlorine atoms in a chlorine molecule. Firstly we calculate the energy required to break $\text{Cl-Cl}$ the bond after that we calculate the required wavelength.

Complete step by step answer: We calculate the energy required to break the $\text{Cl-Cl}$ bond and then calculate the wavelength required to break the $\text{Cl-Cl}$ bond.
Given:
 \[Cl-Cl\text{ }bonding\text{ }energy=243kJmol{{e}^{-1}}\text{ }\]
Here \[h\] is Planck’s constant
 \[h=6.6\times {{10}^{-34}}Js\]
Here \[c\] is the speed of light
 \[c=3\times {{10}^{8}}m{{s}^{-1}}\]
 \[Avogadros\text{ }number=6.023\times {{10}^{23}}mol{{e}^{-1}}\]
The energy required to break one $\text{Cl-Cl}$ bond,
  $=\dfrac{Bond\text{ }energy\text{ }per\text{ }mole}{Avogadros\text{ }number}$
Now we put the value in the formula,
  $\Rightarrow \dfrac{243\times {{10}^{3}}}{6.023\times {{10}^{23}}}J$
  $\Rightarrow 40.36\times {{10}^{-20}}J$
Let the wavelength of the photon required to break one $\text{Cl-Cl}$ bond be$\lambda $.
 \[E=h\nu =h\dfrac{c}{\lambda }\]
After solving we get,
  \[\lambda =\dfrac{hc}{E}\]
Now we put the value in the above equation,
 $\lambda =\dfrac{(6.6\times {{10}^{-34}}Js)(3\times {{10}^{8}}m{{s}^{-1}})}{40.36\times {{10}^{-20}}J}$
After solving we get,
 $\lambda =4.91\times {{10}^{-7}}m$
Here we get the wavelength of light to require to break the bond between two chlorine atoms in a chlorine molecule is$\lambda =4.91\times {{10}^{-7}}m$.

So the correct option is A.

Note: To understand this question we have to study the bond energy. How much energy is required to break the bond $\text{Cl-Cl}$, and the formula is used to find the required energy to break the bond. This question is using the formula \[\lambda =\dfrac{hc}{E}\] to find out the wavelength of light.