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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    For a particle of mass \[m\] enclosed in a one-dimensional box of length\[L\], the de-Broglie concept would lead to stationary waves, with nodes at the two ends. The energy values allowed for such a system (with \[n\] as integer) will be

    A) \[\frac{{{h}^{2}}}{8m{{L}^{2}}}{{n}^{2}}\]                             

    B) \[\frac{{{h}^{2}}}{4m{{L}^{2}}}{{n}^{2}}\]

    C) \[\frac{h}{4mL}n\]                          

    D)  \[\frac{{{h}^{2}}}{4m{{L}^{2}}}{{n}^{2}}\]

    Correct Answer: A

    Solution :

    One dimensional potential well                 \[\lambda =\frac{2L}{n}\]and\[P=\frac{nh}{2L}\] The energy for a system                 \[E=\frac{{{P}^{2}}}{2m}\]                 \[E=\frac{{{n}^{2}}{{h}^{2}}}{8{{L}^{2}}m}\]


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