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Two hydrogen atoms collide in a head on collision and end up with zero kinetic energy. Each then emits a photon of 121.6 nm (n=2 to n=1 transition). At what speed were the atoms moving before the collision?

Answer :

Explanation:

Expression for the kinetic energy is as follows.

         K.E = [tex]\frac{1}{2}mv^{2}[/tex]

Now, total kinetic energy will be as follows.

    K.E = [tex]2 \times \frac{1}{2}mv^{2}[/tex] = [tex]m \times v^{2}[/tex]

Since, this energy converts into electromagnetic radiation of wavelength 121.6 nm.

Relation between energy and photon is as follows.

   Energy of photon = [tex]\frac{hc}{\lambda}[/tex]

                                = [tex]\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{121.6 \times 10^{-9}}[/tex]

                                 = [tex]1.63 \times 10^{-18} J[/tex]

    [tex]m \times v^{2} = 1.63 \times 10^{-18}[/tex]

          v = [tex]\sqrt{\frac{1.63 \times 10^{-18}}{1.67 \times 10^{-27}}[/tex]

             = [tex]3.12 \times 10^{4}[/tex] m/s

Thus, we can conclude that atoms were moving at a speed of [tex]3.12 \times 10^{4}[/tex] m/s before the collision.

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