COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Chapter 32, Problem 6TP
To determine

(a)

To explain:

The equation of helium fusion reaction

Expert Solution
Check Mark

Answer to Problem 6TP

The fusion reaction of helium is given by the following equation −

   (H12)+(H12)(H23 )+(n01 )+Energy

Explanation of Solution

Introduction:

The formation of one or more different atomic nuclei and the subatomic particles by the combination of two or more atomic nuclei under the chemical reaction which is known as the nuclear fusion.

The following are used to achieve the fusion −

  1. Thermonuclear fusion
  2. Inertial confinement fusion
  3. Beam-beam fusion (Beam -target fusion)
  4. Inertial electrostatic confinement
  5. Muon − catalyzed fusion

There are two types of fusion reaction −

  1. First reaction in which the preservation of the neutrons and protons number is available
  2.   D+THe+n

    Where,

    Before the reaction − two protons and three neutrons present at left side, same present at right side also

  3. In second type of reaction − conversion between the protons and neutrons
  4. The initiation of the star burning available and formation of deuterium by the fusion of two hydrogen nuclei

      H+HD+v+β+

    Where,

    Positron − β+

    Neutrinos - v

    Hence, the fusion reaction for helium production is given by −

       (H12)+(H12)(H23 )+(n01 )+Energy

Conclusion:

In nuclear reaction, the energy is released when the mass of resultant particles is lesser than the initial reactant's mass.

To determine

(b)

To calculate:

The difference between the mass of reactants and mass of products is  0.00304u

Expert Solution
Check Mark

Answer to Problem 6TP

Explanation of Solution

Given:

  mdeuterium=2.014102umH23e=3.01603umn01 =1.008665u

Formula used:

  1. The mass of reactants is given by −
  2.   mreactants= mdeuterium+mdeuterium

    Where,

    The mass of deuterium − mdeuterium

  3. The total mass of products is given by −
  4.   mproducts= mH23e+mn01 

    Where,

    The mass of the helium atom − mH23e

    The mass of neutron − mn01 

  5. The difference between the mass of reactant and products is given by −
  6.   Δm = mreactants- mproducts

Calculation:

The mass of parent nuclei is given by −

  mreactants= mdeuterium+mdeuterium

On putting the given values

  mreactants= 2.014102+2.014102

  mreactants= 4.028204u ................... (1)

Now we can calculate the total mass of the products as −

  mproducts= mH23e+mn01 

On putting the values from the given data

  mproducts=3.01603+1.008665

  mproducts=4.0247u ................... (2)

Hence, by using the calculated mass of reactant and product, we are able to calculate difference between their masses −

  Δm = mreactants- mproducts

Put the calculated mass values from eq. (1) and (2) -

  Δm = mreactants- mproductsΔm = 4.028204u - 4.0247uΔm = 0.00304u

Conclusion:

From the above calculations,

The difference between the mass of reactants and mass of products is calculated as  0.00304u

To determine

(c)

To calculate:

The energy produced from fusion reaction

Expert Solution
Check Mark

Answer to Problem 6TP

The energy produced in fusion reaction is 2.838MeV

Explanation of Solution

Given:

Speed of air − c = 3×108m/s

Mass difference between reactant and product - Δm = 0.00304u

Formula Used:

The energy released from fusion reaction is given by

  E = Δmc2

Where,

Speed of air −

Mass difference between reactant and product - Δm 

Calculation:

We know that −

  1u =1.66×10-27kg

The mass difference is converted to kg −

  Δm = 0.00304uΔm =(0.00304×1 .66×10 -27)kgΔm = 5.046×10-27kg

Now we can calculate the produced energy by the fusion reaction −

  E = Δmc2E =(5 .046×10 -27kg)( 3×10 8m/s)2E = 4.541×10-13J

Conclusion:

Hence, the energy produced from the fusion reaction process is calculated as 4.541×10-13J

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Chapter 32 Solutions

COLLEGE PHYSICS

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