(a)
Equation for conservation of energy.
(a)

Answer to Problem 36P
Explanation of Solution
The formula used to calculate the initial rest energy is,
ERi=mic2
- ERi is the initial rest energy
-
c is the
speed of light - mi is the initial mass
The formula used to calculate the final relativistic energy is,
Ei=K.Ei+ERi=K.Ei+mic2
The formula used to calculate the final rest energy is,
ERf=mfc2
- ERf is the final rest energy
- mf is the final mass
The formula used to calculate the final relativistic energy is,
Ef=K.Ef+ERf=K.Ef+mfc2
The formula used to calculate the conservation energy is,
Ei=EfK.Ei+mic2=K.Ef+mfc2
Thus, the equation for conservation of energy is K.Ei+mic2=K.Ef+mfc2.
Conclusion:
The equation for conservation of energy is K.Ei+mic2=K.Ef+mfc2.
(b)
The total mass of initial particle.
(b)

Answer to Problem 36P
Explanation of Solution
Given info:
Mass of U23592 is 235.043923 u.
Mass of n10 is 1.008665 u.
The formula used to calculate the mass of initial particle is,
mi=mU23592+mn10
- mi is the mass of initial particle
- mU23592 is the mass of u23592
- mn10 is the mass of n10
Substitute 235.043923 u for mU23592 and 1.008665 u for mn10 to find mi.
mi=235.043923 u+1.008665 u=236.052588 u
Thus, the total mass of initial particle is 236.052588 u.
Conclusion:
The total mass of initial particle is 236.052588 u.
(c)
The total mass of final particle.
(c)

Answer to Problem 36P
Explanation of Solution
Given info:
Mass of L14857a is 147.932236 u.
Mass of B8735r is 86.9207119 u.
The formula used to calculate the mass of initial particle is,
mf=mL14857a+mB8735r+mn10
- mf is the mass of initial particle
- mL14857a is the mass of L14857a
- mB8735r is the mass of B8735r
Substitute 147.932236 u for mL14857a , 86.9207119 u for mB8735r and 1.008665 u for mn10 to find mf.
mf=147.932236 u+86.9207119 u+1.008665 u=235.861612 u
Thus, the total mass of final particle is 235.861612 u.
Conclusion:
The total mass of final particle is 235.861612 u.
(d)
The difference between the masses.
(d)

Answer to Problem 36P
Explanation of Solution
The formula used to calculate the mass difference is,
Δm=mi−mf
- Δm is the mass is the mass difference
Substitute 236.052588 u for mi and 235.861612 u for mf to find Δm.
Δm=236.052588 u−235.861612 u=0.190976 u
Thus, the mass difference is 0.190976 u.
Conclusion:
The mass difference is 0.190976 u.
(e)
The final kinetic energy in MeV.
(e)

Answer to Problem 36P
Explanation of Solution
Consider the initial kinetic energy as zero, the kinetic energy is equal to the mass difference.
K.Ef=Δm=(0.190976 u)(931.494 MeV1 u)=177.893 MeV
Thus, the final kinetic energy in MeV is 177.893 MeV.
Conclusion:
The final kinetic energy in MeV is 177.893 MeV
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Chapter 26 Solutions
College Physics (Instructor's)
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