Question

The radius of the orbit of an electron in a hydrogenlike atom (atomic number Z) is $4.5a_0$ where $a_0$ is the Bohr radius. Its orbital angular momentum is $ \frac{3h}{2\pi } $. The value of Z is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (A)

According to Bohr’s quantisation condition
$L = \frac{nh}{2\pi }$
Given : $L = \frac{3h}{2\pi } \quad\therefore \frac{3h}{2\pi } = \frac{nh}{2\pi }$ or $n = 3$
Radius of $n^{th}$ orbit for hydrogen-like atom is $r_{n} = \frac{n^{2}}{z}a_{0}$
where $a_{0}$ is the Bohr radius
Here, $r_{n} = 4.5a_{0}$
$\therefore \quad4.5a_{0} = \frac{\left(3\right)^{2}}{Z} a_{0}$ or $Z = \frac{9}{4.5} = 2$