JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Mock Test - Units Dimenstions and Measurment

  • question_answer
    If \[m,\text{ }e,\,\,{{\varepsilon }_{0}},\] h and c denote mass electron, charge of electron. Planck's constant and speed of light, respectively. The dimensions of \[\frac{me_{{}}^{4}}{\varepsilon _{0}^{2}h_{{}}^{3}c}\] are

    A) [\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{-1}\]]                  

    B) [\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{-1}\]]

    C) [\[M_{{}}^{2}L_{{}}^{{}}T_{{}}^{-3}\]]    

    D) [\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{0}\]]

    Correct Answer: D

    Solution :

    [d] In Bohr's model, \[\frac{1}{\lambda }=\frac{m{{e}^{4}}}{{{\varepsilon }_{0}}^{2}{{h}^{3}}c}\left( \frac{1}{{{n}_{1}}^{2}}-\frac{1}{{{n}_{2}}^{2}} \right)\] Where \[\lambda \]=wavelength, \[{{n}_{1}}\]and \[{{n}_{2}}\]are principal quantum numbers. \[\therefore \left[ \frac{m{{e}^{4}}}{{{\varepsilon }_{0}}^{2}{{h}^{3}}c} \right]=[{{L}^{-1}}]=[{{M}^{0}}{{L}^{-1}}{{T}^{0}}]\]


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