A Hydrogen atom and a ion are both in the second excited state. If and are their respective electronic angular momenta, and and their respective energies, then [2002]

Question

A Hydrogen atom and a ${Li}^{+ +}$ 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]

Smart Achievers · Accepted Answer

(2)

$l = \frac{n h}{2 π},$ $| E | \propto \frac{Z^{2}}{n^{2}};$ $n = 3$

$\Rightarrow l_{H} = l_{Li}$ and $| E_{H} | < | E_{Li} |$

Solution

Q.
A Hydrogen atom and a ${Li}^{+ +}$ 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]

1 $ℓ_{H} > ℓ_{L i}$ and $| E_{H} | > | E_{L i} |$

2 $ℓ_{H} = ℓ_{L i}$ and $| E_{H} | < | E_{L i} |$

3 $ℓ_{H} = ℓ_{L i}$ and $| E_{H} | > | E_{L i} |$

4 $ℓ_{H} < ℓ_{L i}$ and $| E_{H} | < | E_{L i} |$

Ans.
(2)

$l = \frac{n h}{2 π},$ $| E | \propto \frac{Z^{2}}{n^{2}};$ $n = 3$

$\Rightarrow l_{H} = l_{Li}$ and $| E_{H} | < | E_{Li} |$

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Solution

Q. A Hydrogen atom and a Li++ 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 [2002]

1 ℓH>ℓLi and |EH|>|ELi|

2 ℓH=ℓLi and |EH|<|ELi|

3 ℓH=ℓLi and |EH|>|ELi|

4 ℓH<ℓLi and |EH|<|ELi|

Ans. (2) l=nh2π, |E|∝Z2n2; n=3 ⇒ lH=lLi and |EH|<|ELi|