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A hydrogen atom, and a doubly ionised lithium (Li)++ atom, are in their first excerted state and the second excited state, respectively. If lH and lLi are the respective angular momenta, and KH , KLi are the, respective, kinetic energies, of the electron, in the two atoms, we can say that

(1) \(\frac{l_H}{l_{Li}}=\frac{2}{3};\frac{K_H}{K_Li}=\frac{2}{3}\)

(2) \(\frac{l_H}{l_{Li}}=\frac{1}{2};\frac{K_H}{K_Li}=\frac{4}{1}\)

(3) \(\frac{l_H}{l_{Li}}=\frac{2}{3};\frac{K_H}{K_Li}=\frac{1}{4}\)

(4) \(\frac{l_H}{l_{Li}}=\frac{1}{2};\frac{K_H}{K_Li}=\frac{9}{4}\)

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 (3) \(\frac{l_H}{l_{Li}}=\frac{2}{3};\frac{K_H}{K_Li}=\frac{1}{4}\)

For the hydrogen atom nH = 2 and zH = 1

For the doubly ionised lithium atom, we have nLi = 3; and zLi = 3

According to Bohr’s first postulate, the angular momentum of electron, in an orbit, is directly proportional to n; therefore;

The K.E of the electron, is an orbit, equals the |T.E| and T.E ∝ z2/n2 ; therefore

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