A neutron with mass my moving with velocity vo collides elastically and head-on with a target particle with mass m₂ that is at rest. After the collision, the neutron moves with velocity vifand the target particle moves with velocity v2f- (a) Consider collisions of the neutron (mass = 1.0 atomic mass units (amu)) with the following stationary target particles 1. an electron (mass = 5.49 x 104 amu) 2. a proton (mass = 1.00 amu) 3. the nucleus of a bismuth atom (mass = 209 amu) 4. the nucleus of a nitrogen atom (mass = 14.0 amu) Match collisions 1-3 above with one of the following head-on collisions that we discussed in lecture: • the collision between two identical billiard balls, one of the billiard balls initially at rest the collision between a ping pong ball and a bowling ball, the ping pong ball initially a rest • the collision between a ping pong ball and a bowling ball, the bowling ball initially at rest (b) Calculate the ratio of the neutron's final kinetic energy to its initial kinetic energy (Ke/Ki)neutron for each of the collisions in (a). (answer: electron: K/K;=0.998: proton: K/K;=0; bismuth: K+/K; = 0.981; nitrogen: K+K;= 0.751) (c) What percentage of the neutron's initial kinetic energy is transferred to each target particle? Hint: Calculate (K) target (Ki)neutron (answer: electron: 0.22%; proton: 100%; bismuth: 1.9%; nitrogen: 25%) (d) Each of the answers to parts (b) and (c) should add up to 100%. Do they?
A neutron with mass my moving with velocity vo collides elastically and head-on with a target particle with mass m₂ that is at rest. After the collision, the neutron moves with velocity vifand the target particle moves with velocity v2f- (a) Consider collisions of the neutron (mass = 1.0 atomic mass units (amu)) with the following stationary target particles 1. an electron (mass = 5.49 x 104 amu) 2. a proton (mass = 1.00 amu) 3. the nucleus of a bismuth atom (mass = 209 amu) 4. the nucleus of a nitrogen atom (mass = 14.0 amu) Match collisions 1-3 above with one of the following head-on collisions that we discussed in lecture: • the collision between two identical billiard balls, one of the billiard balls initially at rest the collision between a ping pong ball and a bowling ball, the ping pong ball initially a rest • the collision between a ping pong ball and a bowling ball, the bowling ball initially at rest (b) Calculate the ratio of the neutron's final kinetic energy to its initial kinetic energy (Ke/Ki)neutron for each of the collisions in (a). (answer: electron: K/K;=0.998: proton: K/K;=0; bismuth: K+/K; = 0.981; nitrogen: K+K;= 0.751) (c) What percentage of the neutron's initial kinetic energy is transferred to each target particle? Hint: Calculate (K) target (Ki)neutron (answer: electron: 0.22%; proton: 100%; bismuth: 1.9%; nitrogen: 25%) (d) Each of the answers to parts (b) and (c) should add up to 100%. Do they?
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![Head-on elastic collisions in one dimension
A neutron with mass m₁ moving with velocity vo collides elastically and head-on with a target
particle with mass me that is at rest. After the collision, the neutron moves with velocity vif and
the target particle moves with velocity v2f.
(a) Consider collisions of the neutron (mass = 1.0 atomic mass units (amu)) with the following
stationary target particles
1. an electron (mass = 5.49 x 10+4 amu)
2. a proton (mass = 1.00 amu)
3. the nucleus of a bismuth atom (mass = 209 amu)
4. the nucleus of a nitrogen atom (mass = 14.0 amu)
Match collisions 1-3 above with one of the following head-on collisions that we discussed in
lecture:
• the collision between two identical billiard balls, one of the billiard balls initially at rest
• the collision between a ping pong ball and a bowling ball, the ping pong ball initially at
rest
the collision between a ping pong ball and a bowling ball, the bowling ball initially at rest
(b) Calculate the ratio of the neutron's final kinetic energy to its initial kinetic energy (K/Ki)neutron
for each of the collisions in (a). (answer: electron: K/K₁=0.998; proton: K/K₁ = 0; bismuth: K+/Ki
= 0.981; nitrogen: K+/K; = 0.751)
(c) What percentage of the neutron's initial kinetic energy is transferred to each target particle?
Hint: Calculate (Kf)target (Ki)neutron.
(answer: electron: 0.22%; proton: 100%; bismuth: 1.9%; nitrogen: 25%)
(d) Each of the answers to parts (b) and (c) should add up to 100%. Do they?
K = ½ mv²
p = mv
vif = [(m1-m2) / (m1 + m2)]vo
v2f = [2m1/(m1 + m2)]vo](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56cdda57-70a5-4d4f-8db2-c3e75050b484%2F122ba68a-8df8-49bc-b4e1-726ec04c8e4a%2Fuc5jku_processed.png&w=3840&q=75)
Transcribed Image Text:Head-on elastic collisions in one dimension
A neutron with mass m₁ moving with velocity vo collides elastically and head-on with a target
particle with mass me that is at rest. After the collision, the neutron moves with velocity vif and
the target particle moves with velocity v2f.
(a) Consider collisions of the neutron (mass = 1.0 atomic mass units (amu)) with the following
stationary target particles
1. an electron (mass = 5.49 x 10+4 amu)
2. a proton (mass = 1.00 amu)
3. the nucleus of a bismuth atom (mass = 209 amu)
4. the nucleus of a nitrogen atom (mass = 14.0 amu)
Match collisions 1-3 above with one of the following head-on collisions that we discussed in
lecture:
• the collision between two identical billiard balls, one of the billiard balls initially at rest
• the collision between a ping pong ball and a bowling ball, the ping pong ball initially at
rest
the collision between a ping pong ball and a bowling ball, the bowling ball initially at rest
(b) Calculate the ratio of the neutron's final kinetic energy to its initial kinetic energy (K/Ki)neutron
for each of the collisions in (a). (answer: electron: K/K₁=0.998; proton: K/K₁ = 0; bismuth: K+/Ki
= 0.981; nitrogen: K+/K; = 0.751)
(c) What percentage of the neutron's initial kinetic energy is transferred to each target particle?
Hint: Calculate (Kf)target (Ki)neutron.
(answer: electron: 0.22%; proton: 100%; bismuth: 1.9%; nitrogen: 25%)
(d) Each of the answers to parts (b) and (c) should add up to 100%. Do they?
K = ½ mv²
p = mv
vif = [(m1-m2) / (m1 + m2)]vo
v2f = [2m1/(m1 + m2)]vo
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