If the ratio of energies of an electron in th | vedclass

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

Question

(B) The energy of an electron in a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.
For the same excited state,$n$

Vedclass · Accepted Answer

$3: 1$

Vedclass · Answer

(B) The energy of an electron in a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.
For the same excited state,$n$ is constant,so $E \propto Z^2$.
Given the ratio of energies $\frac{E_H}{E_{Li^{2+}}} = \frac{1}{9}$,we have $\frac{Z_H^2}{Z_{Li^{2+}}^2} = \frac{1^2}{3^2} = \frac{1}{9}$,which is consistent with the given data.
The radius of an electron in a hydrogen-like species is given by $r_n = 0.529 	imes \frac{n^2}{Z} \mathring{A} $.
For the same excited state,$n$ is constant,so $r \propto \frac{1}{Z}$.
Therefore,the ratio of radii is $\frac{r_H}{r_{Li^{2+}}} = \frac{Z_{Li^{2+}}}{Z_H} = \frac{3}{1} = 3: 1$.

If the ratio of energies of an electron in the excited states of $H$ and $Li^{2+}$ is $1: 9$,the radius ratio of the electron in the same excited states of $H$ and $Li^{2+}$ is

Similar Questions

Which of the following statements is incorrect?

For a hydrogen-like species,the ratio of velocities of electrons in the $I, II,$ and $III$ orbits,i.e.,$V_1 : V_2 : V_3$,will be:

Assertion : The radius of the first orbit of hydrogen atom is $0.529 \ \mathring{A}$.
Reason : Radius of each circular orbit $(r_n) = 0.529 \ \mathring{A} \ (n^2/Z)$,where $n = 1, 2, 3$ and $Z =$ atomic number.

Maximum frequency of emission is obtained for the transition $:-$

Which one of the following is incorrect for the Bohr model of the hydrogen atom?

Vedclass Test Series

Exam Paper Generator

Online Exam Module