Question

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

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (B)

The energy of $n^{th}$ state of a hydrogen like atom is given as
$E_n=\frac{C{Z}^2}{n^2}$, where C is a constant.
For ground state of hydrogen atom, $Z=1,n=1$
$\therefore E_1=\frac{C{\left(1\right)}^2}{{\left(1\right)}^2}=C$
For $n^{th}$ state of $L{i}^{2+}ion\left(Z=3\right);E_n=\frac{C{\left(3\right)}^2}{n^2}=\frac{9C}{n^2}$
As $E_n=E_1\therefore \frac{9C}{n^2}=C$ or $n^2=9$ or $n=3$