Question

Read the passage given below and answer the question The hydrogen-like species $Li^{2+}$ is in a spherically symmetric state $S_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state $S_2$. The state $S_2$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom. Energy of the state $S_1$ in units of the hydrogen atom ground state energy is

• A. $0.75$
• B. $1.50$
• C. $2.25$
• D. $4.50$

Answer 1

Answer: (C)

$2.25$

Answer 2

For $S_1$ state of $Li^{2+}$, $n = 2$ and $Z = 3$. $\therefore$ Energy of the state $S_1$ in the units of hydrogen atom ground state energy is : $E=E_{H}\times\frac{Z^{2}}{n^{2}}$ $E_{H}\times\frac{3^{2}}{2^{2}}$ $=\frac{9}{4}E_{H}$ $=2.25\times E_{H}$