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 : $L=\frac{3h}{2\pi }\therefore \frac{3h}{2\pi }=\frac{nh}{2\pi }$ 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, $r_n=4.5a_0$
$\therefore 4.5a_0=\frac{{\left(3\right)}^2}{Z}{a}_0$ or $Z=\frac{9}{4.5}=2$