Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Question
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Chapter 41, Problem 39P

(a)

To determine

The unknown particle in the reaction.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given: The reaction is p+pΛ0+Κ0+p+(?) .

Introduction:

The reaction process for given particle is balanced if charge, baryon number, lepton numbers and spin are conserved.

The total charge before and after the reaction must be same; it means, the charge must be conserved in the reaction.

Conserve the total charge before and after the reaction.

  +1+1=0+0+1+Q+2=+1+QQ=+1

Here, Q is the charge number of unknown particles.

The Baryon number before and after the reaction must be same; it means, the Baryon number must be conserved in the reaction.

Conserve the Baryon number before and after the reaction.

  +1+1=+1+0+1+B+2=+2+BB=0

Here, B is the baryon number of unknown particles.

The strangeness before and after the reaction must be same; it means, the strangeness must be conserved in the reaction.

Conserve the strangeness before and after the reaction.

  0+0=1+1+0+SS=0

Here, S is the strangeness of unknown particles.

The spin before and after the reaction must be same; it means, the spin must be conserved in the reaction.

Conserve the spin before and after the reaction.

  +12+12=+12+0+12+ss=0

Here, s is the strangeness of unknown particles.

All the above properties illustrate that the unknown particle is pion particle.

Conclusion:

Thus, the unknown particle in the reaction is pion(π+) particle.

(b)

To determine

The Q value for the reaction.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

The reaction is p+pΛ0+Κ0+p+π+ .

Formula used:

Write the expression for change in mass.

  Δm=(mp+mp)(mΛ0+mΚ0+mp+mπ+)

Here, mΛ0 is mass of baryon, mp is mass of proton, mπ+ is mass of pion, mΚ0 is mass of meson and Δm is change in mass.

Write the expression for Q value.

  Q=Δmc2

Substitute (mp+mp)(mΛ0+mΚ0+mp+mπ+) for Δm in above expression.

  Q=[(mp+mp)(mΛ0+mΚ0+mp+mπ+)]c2 …… (1)

Here, Q is the energy released and c is the speed of light.

Calculation:

Substitute 1116MeV/c2 for mΛ0 , 938.3MeV/c2 for mp , 497.7MeV/c2 for mΚ0 and 139.6MeV/c2 for mπ+ in equation (1).

  Q=[(938.3MeV/c2+938.3MeV/c2)(1116MeV/c2+497.7MeV/c2+938.3MeV/c2+139.6MeV/c2)]c2=815MeV

Conclusion:

Thus, the Q value for the reaction is 815MeV .

(c)

To determine

The thresholdenergy for this reaction.

(c)

Expert Solution
Check Mark

Explanation of Solution

Given:

The reaction is p+pΛ0+Κ0+p+π+ .

Formula used:

Write the expression for change in mass.

  Δm=(mp+mp)(mΛ0+mΚ0+mp+mπ+)

Here, mΛ0 is mass of baryon, mp is mass of proton, mπ+ is mass of pion, mΚ0 is mass of meson and Δm is change in mass.

Write the expression for Q value.

  Q=Δmc2

Substitute (mp+mp)(mΛ0+mΚ0+mp+mπ+) for Δm in above expression.

  Q=[(mp+mp)(mΛ0+mΚ0+mp+mπ+)]c2

Here, Q is the energy released and c is the speed of light.

Write the expression for threshold energy.

  Kth=Q2mp(mp+mp+mΛ0+mΚ0+mp+mπ+) …… (2)

Here, Kth is the threshold energy for the reaction.

Calculation:

Substitute 1116MeV/c2 for mΛ0 , 938.3MeV/c2 for mp , 497.7MeV/c2 for mΚ0 , 139.6MeV/c2 for mπ+ and 815MeV for Q in equation (2).

  Kth=815MeV2(938.3MeV/c2)[938.3MeV/c2+938.3MeV/c2+1116MeV/c2+497.7MeV/c2+938.3MeV/c2+139.6MeV/c2]c2=1984MeV(1GeV1000MeV)=1.984GeV

Conclusion:

Thus, the threshold energy for this reaction is 1.984GeV .

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