Find the best tutors and institutes for Class 12 Tuition
Q12.9:
In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius ((1.5 \times 10^{11})) m with orbital speed ((3 \times 10^{4})) m/s. (Mass of earth = ((6.0 \times 10^{24})) kg.)
Solution :
Step 1: Given Variables and Fundamental Constants
- Mass of Earth ($M$): $6.0 \times 10^{24}\ \text{kg}$
- Radius of orbit ($r$): $1.5 \times 10^{11}\ \text{m}$
- Orbital speed ($v$): $3.0 \times 10^{4}\ \text{m/s}$
- Planck's constant ($h$): $6.63 \times 10^{-34}\ \text{J}\cdot\text{s}$
Step 2: Theoretical Framework
According to the Bohr quantization postulate, the angular momentum ($L$) of a revolving body is quantized and must be an integral multiple of the reduced Planck constant ($\hbar = \frac{h}{2\pi}$). The relationship is expressed as:
$L = mvr = n\frac{h}{2\pi}$
[Per Bohr’s Postulate of Angular Momentum Quantization]
Step 3: Derivation of the Quantum Number ($n$)
To find the quantum number $n$, we rearrange the equation to solve for $n$:
$n = \frac{2\pi mvr}{h}$
Step 4: Substitution and Numerical Computation
Substitute the given values into the equation:
$n = \frac{2 \times 3.14159 \times (6.0 \times 10^{24}\ \text{kg}) \times (3.0 \times 10^{4}\ \text{m/s}) \times (1.5 \times 10^{11}\ \text{m})}{6.63 \times 10^{-34}\ \text{J}\cdot\text{s}}$
Calculating the numerator:
$\text{Numerator} = 2 \times 3.14159 \times 6.0 \times 3.0 \times 1.5 \times 10^{(24 + 4 + 11)}$
$\text{Numerator} \approx 169.646 \times 10^{39} = 1.696 \times 10^{41}$
Calculating $n$:
$n = \frac{1.696 \times 10^{41}}{6.63 \times 10^{-34}} \approx 0.2558 \times 10^{75} \approx 2.56 \times 10^{74}$
Step 5: Visualization of Orbital Dynamics
Final Solution: The quantum number characterizing the Earth's revolution is $n \approx 2.56 \times 10^{74}$. This extremely large value indicates that for macroscopic systems, the quantum nature of angular momentum is effectively continuous, aligning with the correspondence principle.
More Questions from Class 12 Physics Atoms EXERCISES
- Q12.1(a): Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model.
- Q12.1(a): Choose the correct alternative from the clues given at the end of the each statement: The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model.
- Q12.1(b): Choose the correct alternative from the clues given at the end of the each statement: (b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force.
- Q12.1(b): Choose the correct alternative from the clues given at the end of the each statement: In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force.
- Q12.1(c): Choose the correct alternative from the clues given at the end of the each statement: (c) A classical atom based on .......... is doomed to collapse.
- Q12.1(c): Choose the correct alternative from the clues given at the end of the each statement: A classical atom based on .......... is doomed to collapse.
- Q12.1(d): Choose the correct alternative from the clues given at the end of the each statement: (d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in ..........
- Q12.1(d): Choose the correct alternative from the clues given at the end of the each statement: An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in ..........
- Q12.1(e): Choose the correct alternative from the clues given at the end of the each statement: (e) The positively charged part of the atom possesses most of the mass in ..........
- Q12.1(e): Choose the correct alternative from the clues given at the end of the each statement: The positively charged part of the atom possesses most of the mass in ..........
- Q12.2: Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?
- Q12.2: Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?
- Q12.3: A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?
- Q12.3: A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?
- Q12.4: The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?
- Q12.4: The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?
- Q12.5: A hydrogen atom initially in the ground level absorbs a photon, which excites it to the $n = 4$ level. Determine the wavelength and frequency of photon.
- Q12.5: A hydrogen atom initially in the ground level absorbs a photon, which excites it to the ((n)) = 4 level. Determine the wavelength and frequency of photon.
- Q12.6(a): (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the $n = 1, 2$, and $3$ levels.
- Q12.6(a): (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the ((n)) = 1, 2, and 3 levels.
- Q12.6(b): (b) Calculate the orbital period in each of these levels.
- Q12.6(b): (b) Calculate the orbital period in each of these levels.
- Q12.7: The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11}$ m. What are the radii of the $n = 2$ and $n = 3$ orbits?
- Q12.7: The radius of the innermost electron orbit of a hydrogen atom is ((5.3 \times 10^{-11})) m. What are the radii of the ((n)) = 2 and ((n)) = 3 orbits?
- Q12.8: A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
- Q12.8: A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
- Q12.9: In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius $1.5 \times 10^{11}$ m with orbital speed $3 \times 10^{4}$ m/s. (Mass of earth = $6.0 \times 10^{24}$ kg.)
CBSE Solutions for Class 12 Physics Atoms
Chapters in CBSE - Class 12 Physics
- Electric Charges and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Waves
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Nuclei
- Semiconductor Electronics
- Communication Systems
Top Tutors who teach Atoms
Top Tutor
Jhilmil, Delhi
20 yrs of
Exp
4 students
153 hrs of classes completed
500
per hour
Online Classes
Student's Home
I have been teaching with excellent and guaranted results. Many of my students have become successful professionals.
Had a good experience with Mr. Rahul; he goes to great lengths to explain the concepts. I would also recommend him for other subjects.
Top Tutor
Malviya Nagar, Delhi
20 yrs of
Exp
4 students
234 hrs of classes completed
600
per hour
Online Classes
I feel myself God-blessed, having been able to guide thousands of students/learners English, as a school subject as well as a language since 1992. I'm glad to notice that these learners have not only been doing well in their respective areas but also excelling in the real-life situations. May God bless them!!
Top Tutor
Tezpur Airpur Area, Tezpur
7 yrs of
Exp
2 students
421 hrs of classes completed
450
per hour
Online Classes
Tutor's home
I am a mathematics teacher. I have been working in schools from last 6-7 years , and i was giving tutions at my home and even in an insitute in delhi from last 5-7 years. I shifted to tezpur,Assam in April 2021. my last job was in air force school hindan and I currently work at Air force school tezpur. i have a degree in msc mathematics and b.ed. i teach mathematics upto class 12. my key skills are in ms office , mathematics project, calligraphy , and can help out students in their various activities.
Top Tutor
Bisrakh, Noida
5 yrs of
Exp
1 student
2 hrs of classes completed
500
per hour
Online Classes
I am counselling psychologist cum PGT Psychology in a leading school in noida. I have worked with prestigious organisations like Ganga ram hospital, apollo hospital, all india women conference as a counselor. As a teacher i have been associated with DPS and other organisations.
Super Tutor
Knowledge Park II, Noida
9 yrs of
Exp
672 students
50577 hrs of classes completed
400
per hour
Online Classes
I have been providing mentorship to students since 9 years fron now and it let helps my students to. score above 90% in boards examination and perform well in jee and neet..
Overall a good experience.
