The radius of 3^{rd} orbit of hydrogen atom i | vedclass

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

Question

(D) The radius of an orbit in a hydrogen-like species is given by the formula: $r_n = a_0 	imes \frac{n^2}{Z}$, where $a_0$ is the Bohr radius, $n$ i

Vedclass · Accepted Answer

$\frac{2}{9} R$

Vedclass · Answer

(D) The radius of an orbit in a hydrogen-like species is given by the formula: $r_n = a_0 	imes \frac{n^2}{Z}$, where $a_0$ is the Bohr radius, $n$ is the principal quantum number, and $Z$ is the atomic number.For the $3^{rd}$ orbit of $H$ atom $(n=3, Z=1)$: $R = a_0 	imes \frac{3^2}{1} = 9 a_0$.For the $2^{nd}$ orbit of $He^{+}$ ion $(n=2, Z=2)$: $r_2 = a_0 	imes \frac{2^2}{2} = 2 a_0$.From the first equation, $a_0 = \frac{R}{9}$.Substituting this into the second equation: $r_2 = 2 	imes (\frac{R}{9}) = \frac{2}{9} R$.

The radius of $3^{rd}$ orbit of hydrogen atom is $R \text{ pm}$. The radius of $2^{nd}$ orbit of $He^{+}$ ion (in $\text{pm}$) is

Similar Questions

In the ground state of $He^{+}$ ion,how much energy must be supplied to the electron so that the second line of the Balmer series is obtained in its spectrum? ................. $eV$

What is the maximum wavelength line in the Lyman series of $He^{+}$ ion?

The ratio of the radii of the first three Bohr orbits is:

The ratio of the area covered by the second orbital to the first orbital is

What is the packet of energy called?

Vedclass Test Series

Exam Paper Generator

Online Exam Module