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Concepts of Physics

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Consider the fusion in helium plasma. Find the temperature at

Concepts of Physics

Class 12

HC Verma Part II

Chapter 1: Heat and Temperature

64 questions

Chapter 2: Kinetic Theory of Gases

100 questions

Chapter 3: Calorimetry

41 questions

Chapter 4: Laws of Thermodynamics

51 questions

Chapter 5: Specific Heat Capacities of Gases

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Chapter 6: Heat Transfer

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Chapter 7: Electric Field and Potential

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Chapter 8: Gauss's Law

46 questions

Chapter 9: Capacitors

94 questions

Chapter 10: Electric Current in Conductors

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Chapter 11: Thermal and Chemical Effects of Electric Current

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Chapter 12: Magnetic field

91 questions

Chapter 13: Magnetic field due to a Current

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Chapter 14: Permanent Magnets

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Chapter 15: Magnetic Properties of Matter

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Chapter 16: Electromagnetic Induction

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Chapter 17: Alternating Current

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Chapter 18: Electromagnetic Waves

30 questions

Chapter 19: Electric Current through Gases

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Chapter 20: Photoelectric Effect and Wave Particle Duality

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Chapter 21: Bohr'a Model and Physics of the Atom

75 questions

Chapter 22: X-rays

59 questions

Chapter 23: Semiconductors and Semiconductor devices

71 questions

Chapter 24: The Nucleus

94 questions

Calculate the Q-values of the following fusion reactions:

(a)_{1}^{2} H +_{1}^{2} H \to_{1}^{3} H +_{1}^{1} H

﻿ (b)_{1}^{2} H +_{1}^{2} H \to_{2}^{3} He + n

﻿ (c)_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He + n

Atomic masses are m (_{1}^{2} H) = 2.014102 u, m (_{1}^{3} H) = 3.016049 u, m (_{2}^{3} He) = 3.016029 u, m (_{2}^{4} He) = 4.002603 u .

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

Calculate the

Q

-value of the fusion reaction

^{4} He +^{4} He =^{8} Be

. Is such a fusion energetically favourable? Atomic mass of

8 Be

8.0053 u

and that of

^{4} He

4.0026 u

(

Use Mass of proton

m_{p} = 1.007276 u

, Mass of

_{1}^{1} H

atom

= 1.007825 u

, Mass of neutron

m_{n} = 1.008665 u

, Mass of electron

=

0.0005486 u \approx 511 keV / c^{2}, 1 u = 931 MeV / c^{2} .)

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Question

Hard

Solving time: 10 mins

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

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Book:

Concepts of Physics (HC Verma Part II)

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Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

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Text solutionVerified

Given:
Average thermal energy, E=1.5kT
Point of coulomb potential energy =2fm
Potential energy is given by

U = \frac{K q _{1} q _{2}}{r} \dots\dots (1)

Here,

K = \frac{1}{4 π \in _{0}} = 9 \times 1 0^{9}

Charge,

q_{1} = q_{2} = 2 \times 1.6 \times 1 0^{- 19} C

Average kinetic energy (E) is given by

E = \frac{3}{2} k T

Here,
k= Boltzman constant
T= Temperature

Equating equation (1) and (2), we get

\frac{k q _{1} q _{2}}{r} = \frac{3}{2} k T \Rightarrow T = \frac{2 K q _{1} q _{2}}{3 k r} = \frac{2 \times 9 \times 1 0 ^{9} \times 4 \times ( 1.6 \times 1 0 ^{- 19} ) ^{2}}{3 \times 1.38 \times 1 0 ^{- 23} \times 2 \times 1 0 ^{- 15}} = 2.23 \times 1 0^{10} K

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Question Text	Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	18

Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.

Text solutionVerified

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