Looking for classes? Ksquare Career Institute, Bengaluru →
In which of the following systems will the radius of the first orbit (n = 1) be minimum -
A
Doubly ionized lithium
B
Singly ionized helium
C
Deuterium atom
D
Hydrogen atom
Detailed Solution
For a hydrogen-like (one electron) system, Bohr radius of the nth orbit: $r_n = 0.529\left(\dfrac{n^2}{Z}\right)$ Å
For n = 1, $r_1 \propto \dfrac{1}{Z}$.
Hydrogen and deuterium: Z = 1, $r_1 = 0.529$ Å
Singly ionised helium ($He^+$): Z = 2, $r_1 = 0.265$ Å
Doubly ionised lithium ($Li^{2+}$): Z = 3, $r_1 = 0.176$ Å
So the radius of the first orbit is minimum for doubly ionised lithium.
For n = 1, $r_1 \propto \dfrac{1}{Z}$.
Hydrogen and deuterium: Z = 1, $r_1 = 0.529$ Å
Singly ionised helium ($He^+$): Z = 2, $r_1 = 0.265$ Å
Doubly ionised lithium ($Li^{2+}$): Z = 3, $r_1 = 0.176$ Å
So the radius of the first orbit is minimum for doubly ionised lithium.