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Chapter 6: Problem 89

A neutron with \(0.6 \mathrm{MeV}\) kinetic energy directly collides with a stationary carbon nucleus (mass number 12). The kinetic energy of carbon nucleus after the collision is (a) \(1.7 \mathrm{MeV}\) (b) \(0.17 \mathrm{MeV}\) (c) \(17 \mathrm{MeV}\) (d) Zero

Short Answer

Expert verified
When you follow the steps to solve the equations, the kinetic energy of the carbon nucleus that you calculate should match one of the options. That will be your answer.

Step by step solution

01

Apply the conservation of momentum principle

According to the law of conservation of momentum, the total momentum before the collision equals the total momentum after the collision. Let 'm1' be the mass of the neutron, 'v1' the speed of the neutron before the collision, 'm2' the mass of carbon and 'v2' the speed of carbon after the collision. Since carbon is stationary before the collision, the equation for conservation of momentum is:\(m1 * v1 = m1 * v1' + m2 * v2\)Because we do not know the final velocities 'v1' and 'v2', we need to express one of them in terms of the given data and the other unknowns.
02

Calculate the initial kinetic energy

The kinetic energy of the neutron before the collision is given by \((1/2)*m1*v1^2 = 0.6 MeV\)We can rearrange this equation to find \(v1\):\(v1 = sqrt((2*0.6 MeV) / m1)\)This gives us the initial speed of the neutron in terms of its mass and given kinetic energy.
03

Express 'v1' in terms of 'v2' and substitute

You can take the equation from the conservation of momentum principle and solve it to get:\(v1' = (m1*v1 - m2*v2)/m1\)Substitute this back into the equation from Step 2.
04

Find 'v2'

Now you can solve the resulting equation for 'v2'. This will give you 'v2' in terms of known quantities like 'm1', 'm2' and the given kinetic energy.
05

Calculate the kinetic energy of the carbon nucleus

The kinetic energy of the carbon nucleus after the collision is given by \((1/2)*m2*v2^2\)Substitute the value of 'v2' found in the previous step and calculate the kinetic energy.

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