NEET Sample Paper NEET Sample Test Paper-1

  • question_answer A proton and a-particle are accelerated through the same potential difference. The ratio of wavelength of the proton to that of an a-particle is:

    A)  \[2\sqrt{2}:1\]           

    B)  \[1:2\sqrt{2}\]

    C)  \[2:1\]                         

    D)  none of these

    Correct Answer: A

    Solution :

    The relation for energy is given by \[E=\frac{1}{2}m\,{{V}^{2}}\]             or         \[\sqrt{2mE}=m\,V\] and relation for wavelength is given by             \[\lambda =\frac{h}{m\upsilon }=\frac{h}{\sqrt{2m\,E}}\] Now for proton    \[{{\lambda }_{p}}=\frac{h}{\sqrt{2\,P\,E}}\]        ?..(i) and for a particle, \[{{\lambda }_{\alpha }}=\frac{h}{\sqrt{2\times 4m\times 2E}}\]    ?.(ii) (mass of \[\alpha \] - particle is 4 times to that of proton) From equation (i) and equation (ii), we get             \[\frac{{{\lambda }_{p}}}{{{\lambda }_{\alpha }}}=\frac{h}{\sqrt{2m\,E}}\times \frac{\sqrt{16m\,E}}{h}\] \[\Rightarrow \]               \[\frac{{{\lambda }_{p}}}{{{\lambda }_{\alpha }}}=\frac{2\sqrt{2}}{1}\] Hence        \[{{\lambda }_{p}}:{{\lambda }_{\alpha }}=2\sqrt{2}:1\]

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