
In Bohr’s model of the hydrogen atom, the radius of the first orbit of an electron is ${r_0}$. Then the radius of the third orbit is?
A) $\dfrac{{{r_0}}}{9}$
B) ${r_0}$
C) $3{r_0}$
D) $9{r_0}$
Answer
144.9k+ views
Hint: Bohr proposed that electrons orbited the nucleus in specific orbits or shells with a fixed radius. According to Bohr’s model, an electron would absorb energy in the form of photons to get excited to a higher energy level. The Bohr model derives a radius for the nth excited state of hydrogen-like atoms.
Formula Used:
We will be using the formula of Radius of the nth orbit of an electron. It is given by ${r_n} = {r_0}\dfrac{{{n^2}}}{Z}$.
Given: In Bohr’s model of the hydrogen atom, the radius of the first orbit is ${r_0}$ and to find the radius of the third orbit.
Complete step by step solution:
The radius of the nth orbit of an electron is given by ${r_n} = {r_0}\dfrac{{{n^2}}}{Z}$
Where, ${r_n}$- Radius of the nth Orbit
${r_0}$- Radius of the first Orbit
Z - Atomic number
\[n\] - Number of orbits
For the hydrogen atom, the Atomic number $Z = 1$
$ \Rightarrow {r_n} = {r_0}{n^2}$
So, for the third orbit $n = 3$
Thus the radius of the third orbit ${r_3} = {r_0} \times {3^2} = 9{r_0}$
The radius of the third orbit is calculated as $9{r_0}$.
Answer is Option (D), $9{r_0}$.
Note: In $1913$, Niel Bohr introduced the atomic hydrogen model. Bohr proposed that electrons travel in specific orbits, shells around the nucleus. The Bohr model is used to describe the structure of hydrogen energy levels. It is the first atomic model to explain the radiation spectra of atomic hydrogen.
Limitation of the Bohr model of the Hydrogen Atom:
It couldn’t explain why spectral lines are more intense.
It doesn’t work well for complex atoms.
Heisenberg’s uncertainty principle contradicts Bohr’s idea of electrons existing in specific orbits with a known velocity and radius.
Formula Used:
We will be using the formula of Radius of the nth orbit of an electron. It is given by ${r_n} = {r_0}\dfrac{{{n^2}}}{Z}$.
Given: In Bohr’s model of the hydrogen atom, the radius of the first orbit is ${r_0}$ and to find the radius of the third orbit.
Complete step by step solution:
The radius of the nth orbit of an electron is given by ${r_n} = {r_0}\dfrac{{{n^2}}}{Z}$
Where, ${r_n}$- Radius of the nth Orbit
${r_0}$- Radius of the first Orbit
Z - Atomic number
\[n\] - Number of orbits
For the hydrogen atom, the Atomic number $Z = 1$
$ \Rightarrow {r_n} = {r_0}{n^2}$
So, for the third orbit $n = 3$
Thus the radius of the third orbit ${r_3} = {r_0} \times {3^2} = 9{r_0}$
The radius of the third orbit is calculated as $9{r_0}$.
Answer is Option (D), $9{r_0}$.
Note: In $1913$, Niel Bohr introduced the atomic hydrogen model. Bohr proposed that electrons travel in specific orbits, shells around the nucleus. The Bohr model is used to describe the structure of hydrogen energy levels. It is the first atomic model to explain the radiation spectra of atomic hydrogen.
Limitation of the Bohr model of the Hydrogen Atom:
It couldn’t explain why spectral lines are more intense.
It doesn’t work well for complex atoms.
Heisenberg’s uncertainty principle contradicts Bohr’s idea of electrons existing in specific orbits with a known velocity and radius.
Recently Updated Pages
Difference Between Vapor and Gas: JEE Main 2024

Area of an Octagon Formula - Explanation, and FAQs

Charle's Law Formula - Definition, Derivation and Solved Examples

Central Angle of a Circle Formula - Definition, Theorem and FAQs

Average Force Formula - Magnitude, Solved Examples and FAQs

Boyles Law Formula - Boyles Law Equation | Examples & Definitions

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

JEE Main Exam Marking Scheme: Detailed Breakdown of Marks and Negative Marking

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Ideal and Non-Ideal Solutions Raoult's Law - JEE

Dual Nature of Radiation and Matter Class 12 Notes: CBSE Physics Chapter 11
