# Physics Class 12 NCERT Solutions: Chapter 12 Atoms Part 5

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Q: 11. Answer the following questions, which help you understand the difference between Thomsonâ€™s model and Rutherfordâ€™s model better.

(A) Is the average angle of deflection of Î±Âparticles by a thin gold foil predicted by Thomsonâ€™s model much less, about the same, or much greater than that predicted by Rutherfordâ€™s model?

(B) Is the probability of backward scattering (i.e., scattering of Î±-particles at angles greater than 90Â°) predicted by Thomsonâ€™s model much less, about the same, or much greater than that predicted by Rutherfordâ€™s model?

(C) Keeping other factors fixed, it is found experimentally that for small thickness t, the number of Î±-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on provide?

(D) In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of Î±-particles by a thin foil?

Answer:

(A) About the same

The average angle of deflection of Î±Â-particles by a thin gold foil predicted by Thomsonâ€™s model is about the same size as predicted by Rutherfordâ€™s model. This is because the average angle was taken in both models.

(B) Much less

The probability of scattering of Î±-particles at angles greater than predicted by Thomsonâ€™s model is much less than that predicted by Rutherfordâ€™s model.

(C) Scattering is mainly due to single collisions. The chances of a single collision increases linearly with the number of target atoms. Since the number of target atoms increase with an increase in thickness, the collision probability depends linearly on the thickness of the target.

(D) Thomsonâ€™s model

It is wrong to ignore multiple scattering in Thomsonâ€™s model for the calculation of average angle of scattering of Î±Â-particles by a thin foil. This is because a single collision causes very little deflection in this model. Hence, the observed average scattering angle can be explained only by considering multiple scattering.

Q: 12. The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.

Answer:

Radius of the first Bohr orbit is given by the relation,

Where,

Permittivity of free space

r = Distance between the electron and the proton

Coulomb attraction between an electron and a proton is given as:

Gravitational force of attraction between an electron and a proton is given as:

Where,

Gravitational constant

If the electrostatic (Coulomb) force and the gravitational force between an electron and a proton are equal, then we can write:

Putting the value of equation (4) in equation (1), we get:

It is known that the universe is billion light years wide or wide. Hence, we can conclude that the radius of the first Bohr orbit is much greater than the estimated size of the whole universe.