Home
NCERT Soltions
Class 12
Physics
Atoms
(a) Using the Bohr’s model calculate the speed of the electron i...

(a) Using the Bohr’s model calcula | Class 12 Physics Chapter Atoms, Atoms NCERT Solutions

Welcome to the NCERT Solutions for Class 12 Physics - Chapter Atoms. This page offers a step-by-step solution to the specific question from Exercise 1, Question 7: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 7:

(a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels.

(b) Calculate the orbital period in each of these levels.

Answer:

(a) Let ν₁ be the orbital speed of the electron in a hydrogen atom in the ground state level, n₁ = 1. For charge (e) of an electron, ν₁ is given by the relation,

ν₁ = e²/n₁4πϵ₀(h/2π) = e²/2ϵ₀h

Where, e = 1.6 × 10⁻¹⁹ C

ϵ₀ = Permittivity of free space = 8.85 × 10^-12 N⁻¹ C² m⁻²

h = Planck’s constant = 6.62 × 10⁻³⁴ Js

∴ ν₁ = (1.6x10^-19)2/2x8.85x10^-12x6.62x10^-34 = 0.0218 x 10⁸ = 2.18 x 10⁶ m/s

For level n₂ = 2, we can write the relation for the corresponding orbital speed as:

ν₂ = e²/n₂2ϵ₀h = (1.6x10^-19)2/2x2x8.85x10^-12x6.62x10^-34 = 1.09 x 10⁶ m/s

And, for n₃ = 3, we can write the relation for the corresponding orbital speed as:

ν₃ = e²/n₃2ϵ₀h = (1.6x10^-19)2/3x2x8.85x10^-12x6.62x10^-34 = 7.27 x 10⁵ m/s

Hence, the speed of the electron in a hydrogen atom in n = 1, n=2, and n=3 is 2.18 × 10 ⁶ m/s, 1.09 × 10 ⁶ m/s, 7.27 × 10 ⁵ m/s respectively.

(b) Let T ₁ be the orbital period of the electron when it is in level n₁ = 1.

Orbital period is related to orbital speed as:

T₁ = 2πr₁/ν₁

Where, r₁ = Radius of the orbit

= n₁²h²ϵ₀/πme²

h = Planck’s constant = 6.62 × 10⁻³⁴ Js

e = Charge on an electron = 1.6 × 10⁻¹⁹ C

ϵ₀ = Permittivity of free space = 8.85 × 10⁻¹² N⁻¹ C² m⁻²

m = Mass of an electron = 9.1 × 10⁻³¹ kg

∴ T₁ = 2πr₁/ν ₁

= (2πx(1)²x(6.62x10^-34)2x8.85x10^-12)/2.18x10⁶xπx9.1x10^-31x(1.6x10^-19)²

= 15.27x10^-17 = 1.527x10^-16 s

For level n ₂ = 2, we can write the period as:

T₂ = 2πr₂/ν ₂

Where, r₂ = Radius of the electron in n₂ = 2

= (n₂)²h²ϵ₀/πme²

∴ T₂ = 2πr₂/ν₂

= (2πx(2)²x(6.62x10^-34)²x8.85x10^-12)/1.09 x 10⁶ x π x 9.1 x 10^-31 x (1.6 x 10^-19)²

= 1.22 x 10^-15 s

And, for level n₃ = 3, we can write the period as:

T₃ = 2πr₃/ν ₃

Where, r ₃ = Radius of the electron in n₃ = 3

= (n₃)²h²ϵ₀/πme²

∴ T₃ = 2πr₃/ν ₃

= (2πx(3)²x(6.62x10^-34)2x8.85x10^-12)/7.27 x 10⁵ x π x 9.1 x 10^-31 x (1.6 x 10^-19)²

= 4.12 x 10^-15 s

Hence, the orbital period in each of these levels is 1.52 × 10 ⁻¹⁶ s, 1.22 × 10 ⁻¹⁵ s, and 4.12 × 10 ⁻¹⁵ s respectively.

Other Questions of Chapter Atoms

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

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 × 10¹¹ m with orbital speed 3 × 10⁴ m/s. (Mass of earth = 6.0 × 10²⁴ kg.)

What is the shortest wavelength present in the Paschen series of spectral lines?

The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?

Q: Choose the correct alternative from the clues given at the end of the each statement:
(a) The size of the atom in Thomsons model is .......... the atomic size in Rutherfords model. (much greater than/no different from/much less than.)
(b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomsons model/ Rutherfords model.)
(c) A classical atom based on .......... is doomed to collapse. (Thomsons model/ Rutherfords model.)
(d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomsons model/ Rutherfords model.)
(e) The positively charged part of the atom possesses most of the mass in .......... (Rutherfords model/both the models.)

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 the photon.

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?

A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

The radius of the innermost electron orbit of a hydrogen atom is 5.3 ×10 ⁻¹¹ m. What are the radii of the n = 2 and n =3 orbits?

Popular questions of class 12 Physics

What is the force between two small charged spheres having charges of 2 x 10^-7 C and 3 x 10^-7 C placed 30 cm apart in air?

An infinite line charge produces a field of 9 × 10⁴ N/C at a distance of 2 cm. Calculate the linear charge density.

A polythene piece rubbed with wool is found to have a negative charge of 3 × 10⁻⁷ C.

(a) Estimate the number of electrons transferred (from which to which?)

(b) Is there a transfer of mass from wool to polythene?

A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10^-12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

Q: A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.

A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)

A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 10³ N/C and points radially inward, what is the net charge on the sphere?

A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?

Recently Viewed Questions of Class 12 Physics

A short bar magnet has a magnetic moment of 0.48 J T^-1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on (a) the axis, (b) the equatorial lines (normal bisector) of the magnet.

If the bar magnet in exercise 5.13 is turned around by 180º, wherewill the new null points be located?

In a chamber, a uniform magnetic field of 6.5 G (1 G = 10^-4 T) is maintained. An electron is shot into the field with a speed of 4.8 x 10⁶m s^-1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.6 x 10^-19 C, m_e= 9.1 x 10^-31 kg)

In a Young’s double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

The number density of free electrons in a copper conductor estimated in Example 3.1 is 8.5 x 10²⁸ m^-3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 x 10^-6 m² and it is carrying a current of 3.0 A.

An electric dipole with dipole moment 4 × 10⁻⁹ C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 10⁴N C⁻¹. Calculate the magnitude of the torque acting on the dipole.

A storage battery of emf 8.0 V and internal resistance 0.5 Ω is being charged by a 120 V dc supply using a series resistor of 15.5 Ω. What is the terminal voltage of the battery during charging? What is the purpose of having a series resistor in the charging circuit?

A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6.0 x 10^-7 m², and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?

Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

(a) Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What is the total resistance of the combination?

(b) If the combination is connected to a battery of emf 20 V and negligible internal resistance, determine the current through each resistor, and the total current drawn from the battery.

Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Atoms.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Latest Blog Posts

Stay updated with our latest educational content and study tips

The Hidden Risks of Online Gaming for Children — Is your child safe while gaming online?

Online gaming has rapidly become one of the most popular pastimes among children. Whether it’s multiplayer mobile games , PC adventures or console challenges , kids are spending more time than ever in the virtual world . On the surface, gaming seems entertaining and even educational – improving hand- eye coordination , teamwork and problem […]

The Role of Parents in Digital Literacy – Guiding Kids for a Smarter Online Future

Kids today are surrounded by screens from the moment they wake up . Whether it’s smart classrooms, online lessons or video games with friends technology has quietly become a part of everything they do. It’s amazing how much they can learn, explore and create with just a tap or a click. But it also brings […]

How to Recognize and Prevent Online Scams Targeting Kids

The internet is full of entertaining apps, games and movies for kids of all ages. However not everything online is safe. Hidden among these entertaining platforms are internet frauds that target children with phony gifts, free game currencies or friendly looking people. As a parent, you may believe that scammers only target adults; yet children […]

How to Talk to Kids About Screen Time rules Without Conflict

Did you know? The average teenager spends 7 – 8 hours daily on screens . That’s almost like working a full – time job in front of a screen – except kids aren’t earning a paycheck; instead they’re often trading sleep, focus and health for digital time. In today’s world, screens are everywhere – TV, […]

View All Blog Posts