Radius of 1^{st} orbit of H and some orbit of | vedclass

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

Question

(A) The radius of the $n^{th}$ orbit is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
For $H$ atom,$Z = 1$ and $n = 1$,so $r_H = 0.529

Vedclass · Accepted Answer

$-54.4$

Vedclass · Answer

(A) The radius of the $n^{th}$ orbit is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
For $H$ atom,$Z = 1$ and $n = 1$,so $r_H = 0.529 	imes \frac{1^2}{1} = 0.529 \ \mathring{A}$.
For $Be^{3+}$ ion,$Z = 4$. Let the orbit number be $n$.
Given $r_H = r_{Be^{3+}}$,so $0.529 	imes \frac{1^2}{1} = 0.529 	imes \frac{n^2}{4}$.
$1 = \frac{n^2}{4} \implies n^2 = 4 \implies n = 2$.
The energy of an orbit is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ 	ext{eV}$.
For $Be^{3+}$,$Z = 4$ and $n = 2$,so $E = -13.6 	imes \frac{4^2}{2^2} = -13.6 	imes \frac{16}{4} = -13.6 	imes 4 = -54.4 \ 	ext{eV}$.

Radius of $1^{st}$ orbit of $H$ and some orbit of $Be^{3+}$ is same. Energy of their orbit of $Be^{3+}$ is ............$eV$.

Similar Questions

What is the approximate angular momentum (in $J \ s$) of an electron in a hydrogen atom in its ground state? $(h = 6.625 \times 10^{-34} \ J \ s)$

Bohr's atomic model explains the spectrum of only $.......$.

The ratio of the time period of an electron in the first and third orbit of an $H$-atom would be:

The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \ \mathring{A}$. The radius for the first excited state $(n = 2)$ orbit is ........... $\mathring{A}$

The wavelength of the second line of the Balmer series of a hydrogen atom is $\lambda \ nm$. What is the wavelength of the first line of the Lyman series of the $He^{+}$ ion (in $nm$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module