Estimate the temperature needed to achieve the fusion of deuterium to make an α particle. The energy required can be estimated from Coulomb’s Jaw [use the form E = 9.0 × 10 9 ( Q 1 Q 2 / r ), using Q = 1.6 × 10 −19 C for a proton, and r = 2 × 10 −15 m for the helium nucleus; the unit for the proportionality constant in Coloumb’s law is J ∙ m/C 2 ].

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Interpretation Introduction Interpretation: The temperature needed to achieve the fusion of deuterium to make an alpha particle is to be calculated. Concept introduction: The coulombs law expresses the electrostatic force between the two charged particles. Coulombs energy barrier is the energy required to overcome a barrier by the two nuclei to come in close contact with each other to make a nuclear reaction possible. To determine: The temperature needed to achieve the fusion of deuterium to make an alpha particle. Explanation Explanation The energy of coulombs barrier is calculated by the formula, E = K × Q 1 × Q 2 r Where, K is the proportionality constant. r is the nuclear separation. The charge of the particles Q 1 = Q 2 = 1.6 × 10 − 19 C . The value of r is 2 × 10 − 15 m . The value of K is 9 × 10 9 J ⋅ m ⋅ C -2 . Substitute the value of Q 1 , Q 2 , r and K in the above equation. E = 9 × 10 9 J ⋅ m ⋅ C -2 × ( 1.6 × 10 − 19 C ) 2 2 × 10 − 15 m E = 1.152 × 10 − 13 J/nucleus The conversion of J/nucleus to J/mole is done as, 1 mole = 6.023 × 10 23 nucleus Therefore, the conversion of 1.152 × 10 − 13 J/nucleus into J/mole is, 1

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Chemistry: An Atoms First Approach

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Steven S. Zumdahl + 1 other

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Chemistry: An Atoms First Approach

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Steven S. Zumdahl + 1 other

Publisher: Cengage Learning

ISBN: 9781305079243

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Interpretation Introduction

Interpretation: The temperature needed to achieve the fusion of deuterium to make an alpha particle is to be calculated.

Concept introduction: The coulombs law expresses the electrostatic force between the two charged particles.

Coulombs energy barrier is the energy required to overcome a barrier by the two nuclei to come in close contact with each other to make a nuclear reaction possible.

To determine: The temperature needed to achieve the fusion of deuterium to make an alpha particle.

Explanation of Solution

Explanation

The energy of coulombs barrier is calculated by the formula,

E=K×Q1×Q2r

Where,

K is the proportionality constant.
r is the nuclear separation.

The charge of the particles Q1=Q2=1.6×10−19C .

The value of r is 2×10−15 m .

The value of K is 9×109 J⋅m⋅C-2 .

Substitute the value of Q1,Q2 , r and K in the above equation.

E=9×109 J⋅m⋅C-2×(1.6×10−19C)22×10−15 mE=1.152×10−13 J/nucleus

The conversion of J/nucleus to J/mole is done as,

1 mole=6.023×1023nucleus

Therefore, the conversion of 1.152×10−13 J/nucleus into J/mole is,

1

Chemistry: An Atoms First Approach

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