A particle of mass m, is fired at a stationary particle of mass mg, and a reaction takes place in which new particles are created out of the incident kinetic energy. Taken together, the product particles have total mass mg. The minimum kinetic energy the bombarding particle must have so as to induce the reaction is called the threshold energy. At this energy, the kinetic energy of the products is a minimum, so the fraction of the incident kinetic energy that is available to create new particles is a maximum. This condition is met when all the product particles have the same velocity and the particles have no kinetic energy of motion relative to one another. (a) By using conservation of relativistic energy and momentum and the relativistic energy-momentum relation, show that the threshold kinetic energy is [m- (m, + m,)*]c² K. min 2m, Calculate the threshold kinetic energy for each of the following reactions: (b) p + p → p + p + p + p (one of the initial protons is at rest, and antiprotons are produced); (c) T +p → K° + A° (the proton is at rest, and strange particles are produced); (d) p + p –→ p+p+ n° (one of the initial protons is at rest, and pions are produced); and (e) p +p - z° (one of the initial particles is at rest, and Z° particles of mass 91.2 GeV/c² are produced).
A particle of mass m, is fired at a stationary particle of mass mg, and a reaction takes place in which new particles are created out of the incident kinetic energy. Taken together, the product particles have total mass mg. The minimum kinetic energy the bombarding particle must have so as to induce the reaction is called the threshold energy. At this energy, the kinetic energy of the products is a minimum, so the fraction of the incident kinetic energy that is available to create new particles is a maximum. This condition is met when all the product particles have the same velocity and the particles have no kinetic energy of motion relative to one another. (a) By using conservation of relativistic energy and momentum and the relativistic energy-momentum relation, show that the threshold kinetic energy is [m- (m, + m,)*]c² K. min 2m, Calculate the threshold kinetic energy for each of the following reactions: (b) p + p → p + p + p + p (one of the initial protons is at rest, and antiprotons are produced); (c) T +p → K° + A° (the proton is at rest, and strange particles are produced); (d) p + p –→ p+p+ n° (one of the initial protons is at rest, and pions are produced); and (e) p +p - z° (one of the initial particles is at rest, and Z° particles of mass 91.2 GeV/c² are produced).
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![A particle of mass m, is fired at a stationary particle of mass
mg, and a reaction takes place in which new particles are
created out of the incident kinetic energy. Taken together,
the product particles have total mass mg. The minimum
kinetic energy the bombarding particle must have so as to
induce the reaction is called the threshold energy. At this
energy, the kinetic energy of the products is a minimum, so
the fraction of the incident kinetic energy that is available
to create new particles is a maximum. This condition is met
when all the product particles have the same velocity and the
particles have no kinetic energy of motion relative to one
another. (a) By using conservation of relativistic energy and
momentum and the relativistic energy-momentum relation,
show that the threshold kinetic energy is
[m- (m, + m,)*]c²
K.
min
2m,
Calculate the threshold kinetic energy for each of the
following reactions: (b) p + p → p + p + p + p (one of
the initial protons is at rest, and antiprotons are produced);
(c) T +p → K° + A° (the proton is at rest, and strange
particles are produced); (d) p + p –→ p+p+ n° (one of
the initial protons is at rest, and pions are produced); and
(e) p +p - z° (one of the initial particles is at rest, and
Z° particles of mass 91.2 GeV/c² are produced).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddd291c7-9123-481b-8811-d519582c6797%2Fdf6a78c7-50d1-45ad-9a73-3a085a7734e8%2Fnlbhp9w.png&w=3840&q=75)
Transcribed Image Text:A particle of mass m, is fired at a stationary particle of mass
mg, and a reaction takes place in which new particles are
created out of the incident kinetic energy. Taken together,
the product particles have total mass mg. The minimum
kinetic energy the bombarding particle must have so as to
induce the reaction is called the threshold energy. At this
energy, the kinetic energy of the products is a minimum, so
the fraction of the incident kinetic energy that is available
to create new particles is a maximum. This condition is met
when all the product particles have the same velocity and the
particles have no kinetic energy of motion relative to one
another. (a) By using conservation of relativistic energy and
momentum and the relativistic energy-momentum relation,
show that the threshold kinetic energy is
[m- (m, + m,)*]c²
K.
min
2m,
Calculate the threshold kinetic energy for each of the
following reactions: (b) p + p → p + p + p + p (one of
the initial protons is at rest, and antiprotons are produced);
(c) T +p → K° + A° (the proton is at rest, and strange
particles are produced); (d) p + p –→ p+p+ n° (one of
the initial protons is at rest, and pions are produced); and
(e) p +p - z° (one of the initial particles is at rest, and
Z° particles of mass 91.2 GeV/c² are produced).
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