SATHEE: Modern Physics 1 Question 22

Modern Physics 1 Question 22

19. A hydrogen atom and a $L i^{2 +}$ ion are both in the second excited state. If $l_{H}$ and $l_{L i}$ are their respective electronic angular momenta, and $E_{H}$ and $E_{L i}$ their respective energies, then

(2002, 2M)

(a) $l_{H} > l_{L i}$ and $| E_{H} | > | E_{L i} |$

(b) $l_{H} = l_{L i}$ and $| E_{H} | < | E_{L i} |$

(d) $l_{H} < l_{L i}$ and $| E_{H} | < | E_{L i} |$

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Solution:

In second excited state $n = 3$ ,

$\begin{array}{ll} So, & l_{H} = l_{L i} = 3 \frac{h}{2 π} \\ while & E \propto Z^{2} \\ and & Z_{H} = 1, Z_{L i} = 3 \end{array}$

$\begin{array}{ll} So, & | E_{L i} | = 9 | E_{H} | \\ or & | E_{H} | < | E_{L i} | \end{array}$

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Modern Physics 1 Question 22

19. A hydrogen atom and a Li2+ ion are both in the second excited state. If lH and lLi are their respective electronic angular momenta, and EH and ELi their respective energies, then

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19. A hydrogen atom and a $L i^{2 +}$ ion are both in the second excited state. If $l_{H}$ and $l_{L i}$ are their respective electronic angular momenta, and $E_{H}$ and $E_{L i}$ their respective energies, then