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 $243 \,kJ \,mol^{-1} (h = 6.6 \times 10^{-34} Js; c = 3 \times 10^8\, ms^{-1}$, Avogadro’s number = $6.02 \times 10^{-23} mole^{-1}$)

• 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{h c}{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} $
$=4.91 \times 10^{-7}\, m$