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Problems in General Physics

PART SIX. ATOMIC AND NUCLEAR PHYSICS

Q.7. A particle with kinetic energy T is deflected by a spheri

Problems in General Physics

Class 11

IE Irodov

Chapter 1: PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS

277 questions

Chapter 2: PART TWO. THERMODYNAMICS AND MOLECULAR PHYSICS

9 questions

Chapter 3: PART THREE. ELECTRODYNAMICS

46 questions

Chapter 4: PART FOUR. OSCILLATIONS AND WAVES

155 questions

Chapter 5: PART FIVE. OPTICS

215 questions

Chapter 6: PART SIX. ATOMIC AND NUCLEAR PHYSICS

271 questions

Q.7. A point source is suspended at a height h = 1.0 m over the centre of a round table of radius R = 1.0 m. The luminous intensity I of the source depends on direction so that illuminance at all points of the table is the same. Find the function I (θ), where θ is the angle between the radiation direction and the vertical, as well as the luminous flux reaching the table if I (0) = I₀ = 100 cd.

Q.7. A particle with kinetic energy T is deflected by a spherical potential well of radius R and depth U_o, i.e. by the field in which the potential energy of the particle takes the form where r is the distance from the centre of the well. Find the relationship between the aiming parameter b of the particle and the angle 0 through which it deflects from the initial motion direction.

Q.8. A stationary ball of radius R is irradiated by a parallel stream of particles whose radius is r. Assuming the collision of a particle and the ball to be elastic, find:
(a) the deflection angle θ of a particle as a function of its aiming parameter b;
(b) the fraction of particles which after a collision with the ball are scattered into the angular interval between θ and θ + dθ;
(c) the probability of a particle to be deflected, after a collision with the ball, into the front hemisphere

θ < \frac{π}{2}

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Solving time: 5 mins

Q.7. A particle with kinetic energy T is deflected by a spherical potential well of radius R and depth U_o, i.e. by the field in which the potential energy of the particle takes the form where r is the distance from the centre of the well. Find the relationship between the aiming parameter b of the particle and the angle 0 through which it deflects from the initial motion direction.

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Problems in General Physics (IE Irodov)

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Q.7. A particle with kinetic energy T is deflected by a spherical potential well of radius R and depth U_o, i.e. by the field in which the potential energy of the particle takes the form

where r is the distance from the centre of the well. Find the relationship between the aiming parameter b of the particle and the angle 0 through which it deflects from the initial motion direction.

9 mins ago

Discuss this question LIVE

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Text solutionVerified

See the diagram on the next page. In the region where potential is nonzero, the kinetic energy of the particle is, by energy conservation, ____________ T + U₀and the momentum of the particle has the magnitude

2 m (T + U_{0}

. . On the boundary the force is radial, so the tangential component of the momentum does not change :

2 m T s in α = 2 m (T + U_{0} sin φ

sin φ = \frac{T}{T + U _{0}} sin α = \frac{s i n α}{n}

where

n = 1 + \frac{U _{0}}{T}

We also have

θ = 2 (α - φ)

Therefore

sin \frac{θ}{2} = sin (α - φ) = sin α cos φ - cos α sin φ

= sin α (cos φ - \frac{c o s α}{n})

\frac{n s i n θ /2}{s i n α} = n^{2} - sin^{2} α - cos α

(\frac{n s i n θ /2}{s i n α} + cos α)^{2} = n^{2} - sin^{2} α

n^{2} sin^{2} \frac{θ}{2} cot^{2} α + 2 n sin \frac{θ}{2} cot α + 1 = n^{2} cos^{2} \frac{θ}{2}

cot α = \frac{n c o s \frac{θ}{2} - 1}{n s i n \frac{θ}{2}}

Hence

sin α = \frac{n s i n \frac{θ}{2}}{1 + n ^{2} - 2 n c o s \frac{θ}{2}}

Finally, the impact parameter is

b = R sin α = \frac{n R s i n \frac{θ}{2}}{1 + n ^{2} - 2 n c o s \frac{θ}{2}}

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Question Text	Q.7. A particle with kinetic energy T is deflected by a spherical potential well of radius R and depth U_o, i.e. by the field in which the potential energy of the particle takes the form where r is the distance from the centre of the well. Find the relationship between the aiming parameter b of the particle and the angle 0 through which it deflects from the initial motion direction.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	55

Text solutionVerified

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