Answer to Question #101134 in Atomic and Nuclear Physics for Tosin

Question

The molecule of Cl2 (molar mass ( ) 2 µ Cl = 70 g/mole) with velocity v = 300 m/s, absorbs a photon with the wavelength λ = 380 nm,. As the result the molecule splits into 2 separate atoms. One of them obtains the velocity 1 v = 1000 m/s orthogonal to the initial velocity of the molecule. What was the binding energy of the molecule? The pulse of the photon may be neglected. Please, express result is Joules, multiplied by the factor 19 10 and write it down rounded up to 3 significant digits.

Answer 1

Use the law of conservation of energy. Calculate the initial energy of the system. It is kinetic energy of the molecule and energy of the photon:

$$E_1=\frac{m_iv_i^2}{2}+\frac{hc}{\lambda}.$$

The final energy of the system consists of kinetic energy of the atoms and molecule's binding energy $B$. Since they are equal, according to momentum conservation principle, they both will have equal velocities. Hence, we can write:

$$E_2=2\cdot\frac{m_fv_f^2}{2}+B=2\cdot\frac{(m_i/2)\cdot v_f^2}{2}+B=\frac{m_iv_f^2}{2}+B.$$

Therefore:

$$\frac{m_iv_f^2}{2}+B=\frac{m_iv_i^2}{2}+\frac{hc}{\lambda},\\ \space\\ B=\frac{m_i}{2}(v_i^2-v_f^2)+\frac{hc}{\lambda}=\\ \space\\ =\frac{1.66\cdot10^{-27}\cdot70}{2}(300^2-1000^2)+\frac{6.64\cdot10^{-34}\cdot3\cdot10^8}{380\cdot10^{-9}}=\\ \space\\ =4.70\cdot10^{-19}\text{ J}.$$