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Problems in General Physics

PART SIX. ATOMIC AND NUCLEAR PHYSICS

Q.234. A stationary Pb^{200} nucleus emits an alpha-particle w

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.233. (a) What isotope is produced from the alpha-radioactive

R a^{228}

as a result of five alpha-disintegrations and four β-disintegrations?
(b) How many alpha- and β-decays does

U^{238}

experience before turning finally into the stable

P b^{206}

isotope?

Q.234. A stationary

P b^{200}

nucleus emits an alpha-particle with kinetic energy T_α = 5.77 MeV. Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?

Q.235. Find the amount of heat generated by 1.00 mg of a

P o^{210}

preparation during the mean lifetime period of these nuclei if the emitted alpha-particles are known to possess the kinetic energy 5.3 MeV and practically all daughter nuclei are formed directly in the ground state.

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Question

Hard

Solving time: 5 mins

Q.234. A stationary $P b^{200}$ nucleus emits an alpha-particle with kinetic energy T_α = 5.77 MeV. Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?

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Problems in General Physics (IE Irodov)

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Q.234. A stationary

P b^{200}

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Text solutionVerified

The momentum of the a-particle is

2 M_{α} T

This is also the recoil momentum of the daughter nuclear in opposite direction. The recoil velocity of the daughter ntideus is

\frac{2 M _{a} T}{M _{d}} = \frac{2}{196} \frac{2 T}{M _{p}} = 3.39 \times 1 0^{5} m / s

\frac{M _{a}}{M _{d}} T

The energy of the daughter nucleus is

\frac{M _{a}}{M _{d}} T

and this represents a fraction

\frac{M _{α} / M _{d}}{1 + \frac{M _{a}}{M _{d}}} = \frac{M _{α}}{M _{a} + M _{d}} = \frac{4}{200} = \frac{1}{50} = 0.02

of total eneigy. Here Md is the mass of the daughter nucleus.

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Question Text	Q.234. A stationary $P b^{200}$ nucleus emits an alpha-particle with kinetic energy T_α = 5.77 MeV. Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	30

Q.234. A stationary $P b^{200}$ nucleus emits an alpha-particle with kinetic energy T_α = 5.77 MeV. Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?

Text solutionVerified

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Q.234. A stationary $P b^{200}$ nucleus emits an alpha-particle with kinetic energy T_α = 5.77 MeV. Find the recoil velocity of a daughter nucleus. What fraction of the total energy liberated in this decay is accounted for by the recoil energy of the daughter nucleus?