An alpha particle with a kinetic energy of 700 mevmev makes...

An alpha particle with a kinetic energy of 7.00 MeV makes a head-on collision with a gold nucleus at rest. a) What is the distance of closest approach of the two particles? (Assume that the gold nucleus remains stationary and that it may be treated as a point charge. The atomic number of gold is 79, and an alpha particle is a helium nucleus consisting of two protons and two neutrons.)

Transcript

00:01 Hi, so we are given that the kinetic energy of alpha particle is equals to 7 .00 mev which we can convert into joule like 7 multiplied by 1 .602 into 10 to the power minus of 13 joules.

00:30 Now charge of alpha particle is known to us charge of alpha particle is equals to plus 2 electrons.

00:46 Charge on the gold particle that is z e is equals to plus of 79 electrons.

00:56 So since alpha particle is directed towards the gold nucleus so its kinetic energy will be equals to the kinetic energy of the alpha particle that is k.

01:08 So therefore we can say that because the positive charge, the positive charge on the gold nucleus is positive of 79 electrons and that on alpha particle is plus 2 electron hence the electrostatic potential energy pe of the alpha particle when at a distance r0 is u and basically this energy u can be given by the formula.

02:06 So let us write down the formula u is equals to 1 by 4 pi epsilon 0 times of the charge of alpha particle that is 2 electrons times of charge of gold that is z e divided by the distance between them r0.

02:28 So as alpha particle approaches gold nucleus so electrostatic repulsive force due to nucleus increases.

02:38 So basically what is happening here the repulsive force f repulsive is going to increase here as it approaches towards the gold and kinetic energy of alpha particles goes converting into the electrostatic potential energy and that is why we can see at distance of r is equals to r0 kinetic energy of alpha particle appears as the potential energy and that is why this ke of alpha should be equals to the potential energy that is u...

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