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  • A hydrogen atom and a   ion are both in the second excited state. If <img alt="l_{\mathrm{H}} \text{ and

A hydrogen atom and a \mathrm{Li}^{2+}  ion are both in the second excited state. If l_{\mathrm{H}} \text{ and } l_{\mathrm{Li}} are their respectively electronic angular momenta, and \mathrm{E}_{\mathrm{H}} \text{ and } \mathrm{E}_{\mathrm{Li}} their respectively energies, then:
 

Option: 1

l_{\mathrm{H}}>l_{\mathrm{Li}} \text{ and }\left|\mathrm{E}_{\mathrm{H}}\right|>\left|\mathrm{E}_{\mathrm{Li}}\right|


Option: 2

l_{\mathrm{H}}=l_{\mathrm{Li}} \text { and }\left|\mathrm{E}_{\mathrm{H}}\right|<\left|\mathrm{E}_{\mathrm{Li}}\right|


Option: 3

l_{\mathrm{H}}=l_{\mathrm{Li}} \text { and }\left|\mathrm{E}_{\mathrm{H}}\right|>\left|\mathrm{E}_{\mathrm{Li}}\right|


Option: 4

l_{\mathrm{H}}<l_{\mathrm{Li}} \text { and }\left|\mathrm{E}_{\mathrm{H}}\right|<\left|\mathrm{E}_{\mathrm{Li}}\right|


Answers (1)

best_answer

In second excited state, \mathrm{n}=3,

So, \mathrm{l_{\mathrm{H}}=l_{\mathrm{Li}}=3\left(\frac{\mathrm{h}}{2 \pi}\right)}

While \mathrm{E} \propto \mathrm{Z}^2  and \mathrm{Z}_{\mathrm{H}}=1, \mathrm{Z}_{\mathrm{Li}}=3 

So, \mathrm{\left|E_{L i}\right|=9\left|E_H\right|}

or \quad\left|\mathrm{E}_{\mathrm{H}}\right|< \left|\mathrm{E}_{\mathrm{Li}} \right|

Posted by

Gaurav

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