The radii of the first,second,third,and fourt | vedclass

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

Question

(A) The radius of the $n^{th}$ Bohr orbit for a hydrogen-like atom is given by the formula $r_n = 0.529 	imes \frac{n^2}{Z} \,\ \mathring{A}$.
For h

Vedclass · Accepted Answer

$0.529 \,\mathring{A}, 2.116 \,\mathring{A}, 4.761 \,\mathring{A}, 8.464 \,\mathring{A}$

Vedclass · Answer

(A) The radius of the $n^{th}$ Bohr orbit for a hydrogen-like atom is given by the formula $r_n = 0.529 	imes \frac{n^2}{Z} \,\ \mathring{A}$.
For hydrogen,the atomic number $Z = 1$,so the formula simplifies to $r_n = 0.529 	imes n^2 \,\mathring{A}$.
For $n = 1$: $r_1 = 0.529 	imes 1^2 = 0.529 \,\mathring{A}$.
For $n = 2$: $r_2 = 0.529 	imes 2^2 = 0.529 	imes 4 = 2.116 \,\mathring{A}$.
For $n = 3$: $r_3 = 0.529 	imes 3^2 = 0.529 	imes 9 = 4.761 \,\mathring{A}$.
For $n = 4$: $r_4 = 0.529 	imes 4^2 = 0.529 	imes 16 = 8.464 \,\mathring{A}$.
Thus,the radii are $0.529 \,\mathring{A}, 2.116 \,\mathring{A}, 4.761 \,\mathring{A}, 8.464 \,\mathring{A}$.

The radii of the first,second,third,and fourth Bohr orbits of hydrogen are respectively:

Similar Questions

For a hydrogen atom,the energy difference between the first and second Bohr orbits is $3B/4$. What is the energy difference between the first and third Bohr orbits?

What will be the number of photons required to obtain $1 \ J$ of energy by radiation having a wavelength of $4000 \ \mathring{A}$?

If the shortest wavelength of the hydrogen atom in the Lyman series is $x$, then the longest wavelength in the Balmer series of $He^+$ is:

The wavelength of a spectral line for an electronic transition is inversely related to

What is the radius of the fourth orbit of a hydrogen atom (in $pm$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module