Question

In which of the following systems will the radius of the first orbit be minimum

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

Answer 1

The correct option is D Doubly ionized lithium

Radius on nth Bohr's orbit is $r=\frac{a_0{n}^2}{Z}$

For the first orbit it is $\frac{a_0}{Z}$. Now $a_0$ being constant here, only Z varies for all the different options. For minimum radius, Z has to be maximum.

For Hydrogen atom Z= 1

For Deuterium atom Z=1

For singly ionized helium Z= 2

And for doubly ionized lithium Z= 3.

So for doubly ionized lithium the radius will be minimum as its Z is maximum.