Question

The velocity of an electron in the first Bohr orbit of a hydrogen atom is equal to the velocity of the electron in the $n^{th}$ Bohr orbit of $L{i}^{2+}$ atom. Find the value of n.

• A. 1
• B. 3
• C. 2
• D. 4

Answer 1

The correct option is B 3

The velocity of an electron in the $n^{th}$ Bohr orbit of a hydrogen like atom is given by:
$v_n=2.189\times {10}^6\frac{Z}{n}m/s$
Z = 1 and n = 1 for H-atom,
Z = 3 and n is unknown for $L{i}^{2+}$.
Equating the values, we get
$\therefore \frac{1}{1}=\frac{3}{n}$
n = 3