Question

In which of the following systems will the radius of the first orbit $(n=1)$ be minimum?

• A. Deuterium atom
• B. Hydrogen atom
• C. Doubly ionized lithium
• D. Singly ionized helium

Answer 1

Answer: (C)

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.