Q15 / 57 · JEE Advanced 2010 (Paper 2) · Chemistry

Paragraph: The hydrogen-like species $\mathrm{Li}^{2+}$ 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.Question: The state $S_1$ is

  • A
    $1 s$
  • Correct answer
    B
    $2 \mathrm{~s}$
  • C
    $2 p$
  • D
    $3 \mathrm{~s}$

Solution

Given : Hydrogen like species, $\mathrm{Li}^{2+}$ Spherically symmetric state, $S_1 \Rightarrow s$-orbital $S_1$ has radial node $1 \Rightarrow 2 s \quad$ (No. of radial node $=1=n-l-1$, so $n=2$ ) Species undergoes state $S_2$ $S_2$ has energy equal to the ground state energy of $\mathrm{H}$-atom $=-13.6 \mathrm{eV}$ So, $\quad-13.6=-13.6\left(\frac{3^2}{n^2}\right)$ $n=3$ Again radial node $=1=n-1-1$ or $1=3-l-1 \quad$ so $\quad l=1$ It suggests $S_2$ is $3 p$

Hence, the correct answer is option: 'B'.

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