This is a very confusing question and I have no idea how to tackle it.
- In a nuclear reactor, neutrons released by nuclear fission must be slowed down before they can trigger additional reactions in other nuclei. To see what sort of material is most effective in slowing (or moderating) a neutron, calculate the ratio of a neutron's final kinetic energy to its initial kinetic energy,Kf/Ki , for a head-on elastic collision with each of the following stationary target particles. (Note: The mass of a neutron is ,m = 1.009u where the atomic mass unit,1u= 1.66x10^-27.
An Electron M= 5.49x10^-4 u = kf/ki
A Proton M= 1.007 u = kf/ki
A lead atom = 207.2 u = kf/ki?
Head on? I wonder what the probability of that is as compared to a scattering collision?
What you need to do here is use the conservation of momentum to see what the reduction in velocity is.
momentum neutronbefore=momentum neutronafter + mmentum other after
1*Vi=1*Vf+Mass*V
V=(Vi-Vf)/massmoderator
put that in the KE equation (assume conservation of energy), solve for (Vf/Vi)^2, and you have it. You should find that the proton will be the best moderator.
Which fact is true during a fission chain reaction? Please provide the responses
To find the ratio of a neutron's final kinetic energy to its initial kinetic energy (Kf/Ki) for a head-on elastic collision with each of the target particles, we can use the conservation of momentum and the conservation of kinetic energy principles.
First, let's consider the conservation of momentum:
Initial momentum (Pi) = Final momentum (Pf)
Since the neutron is initially moving and the target particle is stationary, the initial momentum of the neutron is given by:
Pi = m_neutron * v_neutron
Where:
m_neutron = mass of the neutron
v_neutron = initial velocity of the neutron (which we will assume is v_neutron = vi)
The final momentum of the neutron is given by:
Pf = m_neutron * v_neutron_final
Where:
v_neutron_final = final velocity of the neutron
For an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Pi = Pf
m_neutron * v_neutron = m_neutron * v_neutron_final
Now, let's consider the conservation of kinetic energy:
Initial kinetic energy (Ki) = Final kinetic energy (Kf)
The initial kinetic energy of the neutron is given by:
Ki = (1/2) * m_neutron * v_neutron^2
The final kinetic energy of the neutron is given by:
Kf = (1/2) * m_neutron * v_neutron_final^2
Now, we can set up equations and solve for the ratio Kf/Ki for each target particle.
a) Electron (M = 5.49x10^-4 u):
For the collision between the neutron and the electron, we use the conservation equations:
Pi = Pf:
m_neutron * v_neutron = m_neutron * v_neutron_final
v_neutron = v_neutron_final
Ki = Kf:
(1/2) * m_neutron * v_neutron^2 = (1/2) * m_neutron * v_neutron_final^2
v_neutron^2 = v_neutron_final^2
Taking the ratio of Kf/Ki:
(Kf/Ki) = (v_neutron_final^2) / (v_neutron^2) = 1
Therefore, Kf/Ki = 1 for the collision between a neutron and an electron.
b) Proton (M = 1.007 u):
Using the same conservation equations:
Pi = Pf:
m_neutron * v_neutron = m_neutron * v_neutron_final
v_neutron = v_neutron_final
Ki = Kf:
(1/2) * m_neutron * v_neutron^2 = (1/2) * m_neutron * v_neutron_final^2
v_neutron^2 = v_neutron_final^2
Taking the ratio of Kf/Ki:
(Kf/Ki) = (v_neutron_final^2) / (v_neutron^2) = 1
Therefore, Kf/Ki = 1 for the collision between a neutron and a proton.
c) Lead atom (M = 207.2 u):
Using the same conservation equations:
Pi = Pf:
m_neutron * v_neutron = m_neutron * v_neutron_final
v_neutron = v_neutron_final
Ki = Kf:
(1/2) * m_neutron * v_neutron^2 = (1/2) * m_neutron * v_neutron_final^2
v_neutron^2 = v_neutron_final^2
Taking the ratio of Kf/Ki:
(Kf/Ki) = (v_neutron_final^2) / (v_neutron^2) = 1
Therefore, Kf/Ki = 1 for the collision between a neutron and a lead atom.
In summary, for elastic collisions between a neutron and each of the target particles (electron, proton, and lead atom), the ratio of the neutron's final kinetic energy to its initial kinetic energy (Kf/Ki) is equal to 1 in all cases.
To solve this problem, we need to use the conservation of momentum and energy principles. Here's how you can tackle it:
Step 1: Understand the problem
In a head-on elastic collision, the momentum and kinetic energy of the neutron before the collision should be equal to the momentum and kinetic energy of both particles after the collision. We are given the mass of the neutron (m) and the masses of the three target particles: Electron (me), Proton (mp), and Lead atom (mlead). We want to find the ratio of the neutron's final kinetic energy (Kf) to its initial kinetic energy (Ki) for each collision.
Step 2: Apply conservation of momentum
In an elastic collision, momentum is conserved. Therefore, we can write the equation:
m * v_initial = (M + m) * v_final
Where:
- m is the mass of the neutron
- v_initial is the initial velocity of the neutron
- M is the mass of the target particle
- v_final is the final velocity of both particles after the collision
Step 3: Calculate the velocities
We need to express the masses in terms of atomic mass units (u) to match the units of the neutron's mass. Use the conversion factor provided (1u = 1.66x10^-27 kg) to convert atomic mass units to kilograms.
For the Electron:
me = 5.49x10^-4 u
Multiplying it with the conversion factor, we get:
M = 5.49x10^-4 u * 1.66x10^-27 kg/u = 9.11134x10^-31 kg
For the Proton:
mp = 1.007 u
Multiplying it with the conversion factor, we get:
mp = 1.007 u * 1.66x10^-27 kg/u = 1.67202x10^-27 kg
For the Lead atom:
mlead = 207.2 u
Multiplying it with the conversion factor, we get:
mlead = 207.2 u * 1.66x10^-27 kg/u = 3.43712x10^-25 kg
Step 4: Solve for the velocities and kinetic energies
Now, we can substitute the masses into the momentum conservation equation and solve for the velocities:
For the Electron:
m * v_initial = (M + m) * v_final
(1.009u) * v_initial = (9.11134x10^-31 kg + 1.009u * 1.66x10^-27 kg/u) * v_final
After solving for the final velocity (v_final), we can calculate the ratio of the neutron's final kinetic energy to its initial kinetic energy (Kf/Ki) using the relation:
Kf/Ki = v_final^2 / v_initial^2
Repeat the same process for the Proton and Lead atom targets.
This calculation will provide you with the ratios Kf/Ki for each collision with different target particles.