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The radius of first Bohr orbit of hydrogen atom is 0.529 A. Calculate the radii of (i) the third orbit of He+ ion and (ii) the second orbit of Li2+ ion.

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Radius of nth Bohr orbit, rn\(\frac{n^2b^2}{4 \pi^2 m Ze^2}\)

For hydrogen atom Z = 1, first orbit n = 1

r1\(\frac{b^2}{4 \pi^2 m e^2}\) = 0.529 Å

(i) For He+ ion, Z = 2, third orbit, n = 3

r3(He+) = \(\frac{3^2b^2}{4 \pi^2m \times 2 \times e^2}\)

\(\frac{9}{2}\Big [\frac{b^2}{4 \pi^2me^2} \Big]\) = \(\frac{9}{2} \)x 0.529 = 2.380 Å

(ii) For Li2+ ion, Z = 3, Second orbit, n = 2

r2(Li2+) = \(\frac{2^2b^2}{4 \pi^2 m \times 3 \times e^2}\) = \(\frac{4}{3} \Big[ \frac{b^2}{4 \pi^2 me^2} \Big]\)

\(\frac{4}{3}\)x 0.529 = 0.7053 Å

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