NEET-XII-Physics
43: Bohr's Model and Physics of the Atom
- #4Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against ln(n)
(a) will pass through the origin
(b) will be a straight line with slope 4
(c) will be a monotonically increasing nonlinear curve
(d) will be a circledigAnsr: a,bAns : (a) will pass through the origin
(b) will be a straight line with slope 4
The radius of the nth orbit of a hydrogen atom is given by
`` {r}_{\,\mathrm{\,n\,}}={n}^{2}{a}_{0}``
Area of the nth orbit is given by
`` {A}_{\,\mathrm{\,n\,}}=\,\mathrm{\,\pi \,}{r}_{\,\mathrm{\,n\,}}^{2}=\,\mathrm{\,\pi \,}{n}^{4}{a}_{0}^{2}``
`` {A}_{1}=\,\mathrm{\,\pi \,}{a}_{0}^{2}``
`` \Rightarrow \,\mathrm{\,ln\,}\left(\frac{{A}_{\,\mathrm{\,n\,}}}{{A}_{1}}\right)=\,\mathrm{\,ln\,}\left(\frac{\,\mathrm{\,\pi \,}{n}^{4}{a}_{0}^{2}}{\,\mathrm{\,\pi \,}{a}_{0}^{2}}\right)``
`` \,\mathrm{\,ln\,}\left(\frac{{A}_{\,\mathrm{\,n\,}}}{{A}_{1}}\right)=4\,\mathrm{\,ln\,}n...\left(1\right)``
From the above expression, the graph of ln (An/A1) against ln(n) will be a straight line passing through the origin and having slope 4.
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