Question 100: Atoms & Nuclei

Question

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)

Accepted Answer

The radius of a hydrogen-like ion according to Bohr's atomic model is given by the formula:
$ r = r_0 \frac{n^2}{Z} $
Where:
$ r_0 $ is the first Bohr radius ($ a_0 $)
$ n $ represents the principal quantum number
$ Z $ is the atomic number of the ion
For the ion $ 	ext{Li}^{++} $, the atomic number $ Z = 3 $ and we are considering the ground state, so $ n = 1 $.
Plugging these values into the formula, we get:
$ r = r_0 \frac{1^2}{3} = \frac{r_0}{3} $
This shows that the radius of $	ext{Li}^{++}$ in its ground state is $\frac{1}{3} a_0$, meaning $ X = 3 $.

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Atoms & Nuclei

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \mathrm{Li}^{++} ion in its ground state is given by \frac{1}{X} a_0, where X= __________ (Where \mathrm{a}_0 is the first Bohr's radius.)

Choose the correct answer: