The radius of the first Bohr orbit of the hyd | vedclass

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

Question

(C) The radius of the $n^{	ext{th}}$ orbit of a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \mathring{A}$.For th

Vedclass · Accepted Answer

$(2)$, $Be^{3+}$

Vedclass · Answer

(C) The radius of the $n^{	ext{th}}$ orbit of a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \mathring{A}$.For the first orbit of the hydrogen atom $(n=1, Z=1)$, the radius is $r_1 = 0.529 \mathring{A}$.For the radius of the $n^{	ext{th}}$ orbit of species $X$ to be equal to the first Bohr orbit of hydrogen, we set $r_n = r_1$, which implies $\frac{n^2}{Z} = 1$, or $n^2 = Z$.Testing the options:For $Be^{3+}$, the atomic number $Z = 4$. Substituting $Z=4$ into $n^2 = Z$, we get $n^2 = 4$, which gives $n = 2$.Thus, for $n = 2$ and $X = Be^{3+}$, the condition is satisfied.

The radius of the first Bohr orbit of the hydrogen atom is the same as that of the orbit $(n)$ of a hydrogen-like species $X$. The values of $(n)$ and $X$ respectively are:

Similar Questions

If the shortest wavelength of $H$ atom in Lyman series is $x$,then the longest wavelength in Balmer series of $He^{+}$ is

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is = ....... (Bohr radius $a_0$)

Which one of the following transitions of an electron in a hydrogen atom emits radiation of the lowest wavelength?

Which formula is used to calculate the energy of a species containing $1$ electron?

At what condition is the energy of an electron in an atom considered to be zero?

Vedclass Test Series

Exam Paper Generator

Online Exam Module