An isotope of helium with mass 7 u breaks up from rest into...

An isotope of helium with mass 7 u breaks up from rest into a nucleus of ordinary helium (assume: mass = 6 u) plus a neutron (assume: mass = 1 u). The rest energy liberated in the break-up is 0.8 MeV, which is shared (not equally) by the products. (a) Using energy and momentum conservation, find the kinetic energy of the neutron. MeV (b) The lifetime of the original nucleus is 6.1 x 10^-20 s. What is the minimum width of the range of neutron kinetic energies we would measure in the laboratory as a result of the uncertainty relationship? eV

Transcript

00:01 Hi there, so for this problem we are told that an isotope of ileon with a mass that is given.

00:07 So let's call this the math capital m is equal to 7 units of mass and braids up from res into a nucleus of ordinary helium and we can assume its mass.

00:23 So let's say that the mass of alien is equal to 6 units of mass.

00:31 Plus a neutron.

00:34 So the mass of this neutron is just one units of mass.

00:39 Now the rest energy liberated in the breakup is 0 .8 mega -electron balls, which is shared not equally by the products.

00:50 So using energy and momentum conservation, we need to find the kinetic energy of the neutron.

01:00 So we need to find that kinetic energy of the neutron.

01:03 With that said, the first thing that we are going to use is the expression for the conservation of momentum.

01:13 We know that the initial momentum should be equal to the final momentum.

01:17 Now, since initially we have an isotope of ilion that is at res, so the initial momentum is equal to zero.

01:26 However, the final momentum is going to be equal to the momentums for each particle.

01:36 So for the ilion nucleus and the neutron particle.

01:44 So we will have the mass of ilion times its speed plus the mass of the neutron times its speed.

01:55 Now, what we are going to do in this is.

01:58 This case is to solve for the speed of alien nucleus.

02:06 So from there, we will obtain that that is just minus the mass of the neutron particle times its speed divided by the mass of ilion.

02:19 Now, we just simply substitute the conditions that we have for the mass, or the values that we are given for the mass, so we will have that this is, the mass of neutron is just one, and the mass of aalion is 6.

02:34 So we obtain this condition for these speeds.

02:37 Now with that said, we know that the sum of the kinetic energy of the neutron plus, the kinetic energy of the alien should add to the total value that is liberated during this breakup, which is 0 .8 megalletron balls.

03:00 Now, with that said, we know that the kinetic energy of alien can be written as 1 divided by 2 times the mass of alien nucleus times its speed to the square.

03:16 Now, we just need to simply substitute the condition that we obtain for, well, first, we know, as you can see from this, that the mass of alien is 6 times the mass of the neutron particle.

03:41 So if we substitute that condition in here, that will be 6 times the mass of the neutron particle.

03:50 This times the speed condition that we obtained, the speed of the neutron divided by 6, that to the square...

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