The radius of the 2^{nd} orbit of He^{+} in B | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The radius of an orbit in Bohr's model is given by the formula $r_n = a_0 \frac{n^2}{Z}$,where $n$ is the principal quantum number and $Z$ is the

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) The radius of an orbit in Bohr's model is given by the formula $r_n = a_0 \frac{n^2}{Z}$,where $n$ is the principal quantum number and $Z$ is the atomic number.For $He^{+}$ $(Z=2)$,the radius of the $2^{nd}$ orbit $(n=2)$ is $r_1 = a_0 \frac{2^2}{2} = 2a_0$.For $Be^{3+}$ $(Z=4)$,the radius of the $4^{th}$ orbit $(n=4)$ is $r_2 = a_0 \frac{4^2}{4} = 4a_0$.The ratio $\frac{r_2}{r_1} = \frac{4a_0}{2a_0} = 2$.Since the ratio is $x : 1$,we have $x = 2$.

The radius of the $2^{nd}$ orbit of $He^{+}$ in Bohr's model is $r_1$ and that of the fourth orbit of $Be^{3+}$ is represented as $r_2$. If the ratio $\frac{r_2}{r_1}$ is $x : 1$,then the value of $x$ is .........

Similar Questions

In the hydrogen atom, the radii of the first four Bohr orbits are related as:

An electron in the hydrogen atom excites from the $2^{nd}$ orbit to the $4^{th}$ orbit. The change in angular momentum of the electron is (Planck's constant $h = 6.64 \times 10^{-34} \ J \cdot s$).

The orbital acceleration of an electron in a hydrogen-like atom is given by:

The magnetic moment $(\mu)$ of an electron revolving around the nucleus varies with the principal quantum number $n$ as

The ionisation energy of a hydrogen atom is $13.6 \; eV$. The ionisation energy of a singly ionised helium atom would be ....... $eV$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module