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  • Which energy state of doubly ionised lithium has the same energy as that of the ground state of hydrogen? Given  for lithium

Which energy state of doubly ionised lithium has the same energy as that of the ground state of hydrogen?
Given \mathrm{Z} for lithium =3
 

Option: 1

6


Option: 2

3


Option: 3

4


Option: 4

5


Answers (1)

best_answer


The energy of nth state of a hydrogen like atom is given as
\mathrm{E}_{\mathrm{n}}=\frac{\mathrm{CZ}^2}{\mathrm{n}^2},\text { where } \mathrm{C}is a constant
For ground state of hydrogen atom, \mathrm{Z}=1, \mathrm{n}=1

\therefore \quad \mathrm{E}_1=\frac{\mathrm{C}(1)^2}{(1)^2}=\mathrm{C}

For nth state of  \mathrm{Li}^{2+} ion (\mathrm{Z}=3) ; \mathrm{E}_{\mathrm{n}}=\frac{\mathrm{C}(3)^2}{\mathrm{n}^2}=\frac{9 \mathrm{C}}{\mathrm{n}^2}

As \mathrm{E}_{\mathrm{n}}=\mathrm{E}_1

\therefore \frac{9 \mathrm{C}}{\mathrm{n}^2}=\mathrm{C}

or \mathrm{n}^2=9
or \mathrm{n}=3

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