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Here we will look at an example of subatomic elastic collisions. High-speed neutrons are produced in a nuclear reactor during nuclear fission processes. Before a neutron can trigger additional fissions, it has to be slowed down by collisions with nuclei of a material called the moderator. In some reactors the moderator consists of carbon in the form of graphite. The masses of nuclei and subatomic particles are measured in units called atomic mass units, abbreviated uu, where 1u=1.66×10−27kg1u=1.66×10−27kg. Suppose a neutron (mass 1.0 u) traveling at 2.6×107m/s2.6×107m/s makes an elastic head-on collision with a carbon nucleus (mass 12 u) that is initially at rest. What are the velocities after the collision? a)If the neutron's kinetic energy is reduced to 64/81 of its initial value in a single collision, what is the mass of the moderator nucleus?

Here we will look at an example of subatomic elastic collisions. High-speed neutrons are produced in a nuclear reactor during nuclear fission processes. Before a neutron can trigger additional fissions, it has to be slowed down by collisions with nuclei of a material called the moderator. In some reactors the moderator consists of carbon in the form of graphite. The masses of nuclei and subatomic particles are measured in units called atomic mass units, abbreviated uu, where 1u=1.66×10−27kg1u=1.66×10−27kg. Suppose a neutron (mass 1.0 u) traveling at 2.6×107m/s2.6×107m/s makes an elastic head-on collision with a carbon nucleus (mass 12 u) that is initially at rest. What are the velocities after the collision? a)If the neutron's kinetic energy is reduced to 64/81 of its initial value in a single collision, what is the mass of the moderator nucleus?

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Here we will look at an example of subatomic elastic collisions. High-speed neutrons are produced in a nuclear reactor during nuclear fission processes. Before a neutron can trigger additional fissions, it has to be slowed down by collisions with nuclei of a material called the moderator. In some reactors the moderator consists of carbon in the form of graphite. The masses of nuclei and subatomic particles are measured in units called atomic mass units, abbreviated uu, where 1u=1.66×10−27kg1u=1.66×10−27kg. Suppose a neutron (mass 1.0 u) traveling at 2.6×107m/s2.6×107m/s makes an elastic head-on collision with a carbon nucleus (mass 12 u) that is initially at rest. What are the velocities after the collision?

a)If the neutron's kinetic energy is reduced to 64/81 of its initial value in a single collision, what is the mass of the moderator nucleus?

### Before and After Collision Diagram This diagram demonstrates a simple physics problem involving a collision between a neutron and a carbon nucleus. #### Initial Conditions ("Before") - **Neutron (n)** - Mass (\(m_n\)): 1.0 u (atomic mass unit) - Initial velocity (\(v_{n,i}\)): \(2.6 \times 10^7\) m/s - Symbol: \( \odot \) - **Carbon Nucleus (C)** - Mass (\(m_C\)): 12 u - Initial velocity (\(v_{C,i}\)): 0 m/s - Symbol: \( \bigcirc \) Both objects are moving along the x-axis. The neutron is initially moving towards the right with a specified velocity, while the carbon nucleus is stationary. #### Final Conditions ("After") - After the collision, the neutron and the carbon nucleus exchange velocities. - **Neutron (n)** - Final velocity (\(v_{n,f}\)) is indicated by an arrow pointing to the left, opposite its initial direction. - **Carbon Nucleus (C)** - Final velocity (\(v_{C,f}\)) is indicated by an arrow pointing to the right. This visual representation illustrates the concept of conservation of momentum, showing how two objects behave before and after a collision.
Transcribed Image Text:### Before and After Collision Diagram This diagram demonstrates a simple physics problem involving a collision between a neutron and a carbon nucleus. #### Initial Conditions ("Before") - **Neutron (n)** - Mass (\(m_n\)): 1.0 u (atomic mass unit) - Initial velocity (\(v_{n,i}\)): \(2.6 \times 10^7\) m/s - Symbol: \( \odot \) - **Carbon Nucleus (C)** - Mass (\(m_C\)): 12 u - Initial velocity (\(v_{C,i}\)): 0 m/s - Symbol: \( \bigcirc \) Both objects are moving along the x-axis. The neutron is initially moving towards the right with a specified velocity, while the carbon nucleus is stationary. #### Final Conditions ("After") - After the collision, the neutron and the carbon nucleus exchange velocities. - **Neutron (n)** - Final velocity (\(v_{n,f}\)) is indicated by an arrow pointing to the left, opposite its initial direction. - **Carbon Nucleus (C)** - Final velocity (\(v_{C,f}\)) is indicated by an arrow pointing to the right. This visual representation illustrates the concept of conservation of momentum, showing how two objects behave before and after a collision.
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