JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    A stationary hydrogen atom of mass m in the ground state achieve minimum excitation energy after head-on, inelastic collision with a moving hydrogen atom. Find the velocity of moving hydrogen atom.

    A)  \[{{\left[ \frac{10.2(eV)}{m} \right]}^{1/2}}\]    

    B)  \[{{\left[ \frac{40.8(eV)}{m} \right]}^{1/2}}\]

    C)  \[{{\left[ \frac{20.4(eV)}{m} \right]}^{1/2}}\]    

    D)  \[{{\left[ \frac{40.8(eV)}{1.0078\,m} \right]}^{1/2}}\]

    Correct Answer: B

    Solution :

    \[mu=2mv\]             \[v=u/2\]             \[\Delta E=\frac{1}{2}\,m{{u}^{2}}\,-\frac{1}{2}2m\,\times {{v}^{2}}=\frac{1}{4}m{{u}^{2}}\]             \[=3.4\,-(-13.6\,)eV=10.2\,eV\]             \[\frac{1}{4}m{{u}^{2}}\,=10.2eV\]           \[u=\,{{\left[ \frac{40.8(eV)\,}{m} \right]}^{1/2}}\]


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