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Q. The ratio between Bohr radii are

VMMC MedicalVMMC Medical 2009

Solution:

For hydrogen and H-like atom Bohrs radius of orbit $ {{r}_{n}}=\frac{{{n}^{2}}{{h}^{2}}}{4{{\pi }^{2}}kZm{{e}^{2}}}=\frac{{{n}^{2}}{{h}^{2}}{{\varepsilon }_{0}}}{\pi mZ{{e}^{2}}}=0.53\frac{{{n}^{2}}}{Z}\overset{\text{o}}{\mathop{\text{A}}}\, $ $ \Rightarrow $ $ {{r}_{n}}=\frac{{{n}^{2}}}{Z} $ $ \therefore $ Ratio between Bohr radii $ =1:4:9:... $ where $ n=1,2,3... $