Question

Iodine molecule dissociates into atoms after absorbing light of wavelength $4500\mathring{A}$. If one quantum of light is absorbed by each molecule, calculate the kinetic energy of the iodine atom.

[Given B.E. of $I_2=240kJ/mol,N_A=6\times {10}^{23}$]

• A. $2.16\times {10}^{-20}J$
• B. $4.1\times {10}^{-20}J$
• C. $3.12\times {10}^{-14}J$
• D. $2.16\times {10}^{-22}J$

Answer 1

The correct option is B $4.1\times {10}^{-20}J$

Bond energy of iodine molecules $=240kJ/mol=240\times {10}^{3}J/mol$.

No. of iodine molecules in 1 mole $=$ Avogadro's number $=6\times {10}^{23}$.

Bond energy of 1 iodine molecule $=\frac{240\times {10}^3}{6\times {10}^{23}}=40\times {10}^{-20}J=4\times {10}^{-19}J$.

We know, $E=\frac{hc}{\lambda }=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{4500\times {10}^{-10}}=4.41\times {10}^{-19}J$.

Also, K.E $=\frac{hc}{\lambda }-[B.E.\text{of 1 iodine molecule}]=0.41\times {10}^{-19}=4.1\times {10}^{-20}J$.

Hence, kinetic energy of one iodine molecule is $4.1\times {10}^{-20}J$.