Download Physics 2 Homework 21 2013 In 1909 British physicist

Physics 2 Homework 21 2013
In 1909 British physicist and chemist, Ernest Rutherford, performing (together with Hans
Geiger and Ernst Marsden) experiment on scattering of heavy and positively charged alpha particles
by atoms of gold, found, to his great surprise, that some of the particles were reflected back. He said
that ”It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came
back and hit you...”
Ernest Rutherford (1871-1937).
This indicated that positive charge of an atom as well as most of the atom’s mass was
concentrated in a small volume, which did not agree with the plum pudding model. Rutherford put
forward another model which is called “planetary model”of atom. According to this model the
electrons are revolving around a small positively charged nucleus similar to planets revolving around
the Sun. But this model produced even more questions than the “plum pudding model”. The main
question was: “Why don’t the negative electrons fall to the positive nucleus?”. As long as we try to
think of electron as of a small hard ball there is no answer. The explanation can be done in the frame
of quantum mechanics, the theory which describes the motion of microscopically small particles
such as electrons, protons and neutrons. According to quantum mechanics, the electron is an object
which possesses the properties of both particle and wave. One of the important properties of such an
object is that it does not “like” when we try to confine it in a small volume. As we try to „squeeze‟
it, its energy increases greatly. That is why, in spite of strong attraction force, the electron does not
fall on the nucleus, but surrounds it as a small cloud. The atomic nucleus consists of positively
charged protons and neutral neutrons. Both proton and neutron have close masses: ~1,673x10-27kg
(proton) and ~1,675x10-27kg (neutron).The electron’s mass more than 1000 times smaller: 9.1 x 1031
kg.
Problem:
1. An alpha particle is moving to the atomic nucleus of gold (let us assume that we have a bare
gold nucleus with charge +1.26x10-17C) at a speed 107m/s. How close it will go to the
nucleus before it is pushed back? Please consider the nucleus and the alpha particles as point
charges.
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2. Find the velocities of the alpha particle and the gold atomic nucleus after collision when they
are far away from each other. The mass of the gold nucleus is 3.27x10-25kg, the mass of alpha
particle is 6.64x10-27kg. (before the collision the gold nucleus was at rest in “our” reference
of frame)
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