NEET-XII-Physics

43: Bohr's Model and Physics of the Atom

with Solutions - page 3
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  • #1
    The Bohr radius is given by
    a0=ε0h2πme2. Verify that the RHS has dimensions of length.
    Ans : The dimensions of ε0 can be derived from the formula given below:
    `` a=\frac{{\epsilon }_{0}{h}^{2}}{\,\mathrm{\,\pi \,}m{e}^{2}}=\frac{{\,\mathrm{\,A\,}}^{2}{\,\mathrm{\,T\,}}^{2}{\left({\,\mathrm{\,ML\,}}^{2}{\,\mathrm{\,T\,}}^{-1}\right)}^{2}}{{\,\mathrm{\,L\,}}^{2}{\,\mathrm{\,ML\,}}^{-2}\,\mathrm{\,M\,}{\left(\,\mathrm{\,AT\,}\right)}^{2}}``
    `` =\frac{{\,\mathrm{\,M\,}}^{2}{\,\mathrm{\,L\,}}^{2}{\,\mathrm{\,T\,}}^{-2}}{{\,\mathrm{\,M\,}}^{2}{\,\mathrm{\,L\,}}^{3}{\,\mathrm{\,T\,}}^{-2}}=\,\mathrm{\,L\,}``
    Clearly, a0 has the dimensions of length.
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