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Q.
In which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?
AIPMTAIPMT 2003Atoms
Solution:
Radius of $n$th Bohr's orbit of hydrogen like atom,
$r_{n} \propto \frac{n^{2}}{Z}$
where, $Z$, is atomic number.
For first orbit, $n=1$
$\therefore r_{n} \propto \frac{1}{Z}$
Now, for radius of first orbit to be minimum, its atomic number must be greater. Here in the problem, atomic number $Z$ is greater for doubly ionized lithium and is $Z=3$, Hence, for this system the radius of first orbit will be minimum.