Unit 2 Particles and Waves
Homework 2.1
1. The following strong interaction has been observed.
K− + p → n + X
The K− is a strange meson of quark composition ū s.
The u quark has a charge of +2/3.
The d quark has a charge of −1/3.
(a) Determine the charge of the strange quark.
(b) Use the appropriate conservation law to determine whether particle X is positive, negative or neutral.
(c) State whether particle X is a baryon or a meson. Justify your answer.
2. (a) The equation for a β− decay can be written as:
(i) For each of these four particles, state its name, and where appropriate, its quark composition.
(ii) State the interaction associated with β decay.
(b) In 1995 scientists at CERN created atoms of antihydrogen.
(i) Name the particles that make up an atom of antihydrogen.
(ii) State the charge of an atom of antihydrogen.
(iii) Explain why it is not possible to store atoms of antihydrogen.
3. The apparatus shown in the diagram is designed to accelerate alpha particles.
An alpha particle travelling at a speed of 2·60 × 106 m s−1 passes through a hole in plate A. The mass of an alpha particle is 6·64 × 10−27 kg and its charge is 3·20 × 10−19 C.
(a) When the alpha particle reaches plate B, its kinetic energy has increased to 3·05 × 10−14 J.
Show that the work done on the alpha particle as it moves from plate A to plate B is 8.1 × 10−15 J,
(b) Calculate the potential difference between plates A and B.
(c) The apparatus is now adapted to accelerate electrons from A to B through the same potential difference.
How does the increase in kinetic energy of an electron compare with the increase in kinetic energy of the alpha particle in part (a)? Justify your answer.
4. Identification of elements in a semiconductor sample can be carried out using an electron scanner to release atoms from the surface of the sample for analysis. Electrons are accelerated from rest between a cathode and anode by a potential difference of 2·40 kV.
A variable voltage supply connected to the deflection plates enables the beam to scan the sample between points A and B shown in the figure below.
(a) Calculate the speed of the electrons as they pass through the anode.
(b) Explain why the electron beam follows:
(i) a curved path between the plates;
(ii) a straight path beyond the plates.
(c) The anode voltage is now increased. State what happens to the length of the sample scanned by the electron beam. You must justify your answer.
5. A cyclotron is a particle accelerator which consists of two D-shaped hollow structures, called “dees”, placed in a vacuum.
The diagram below shows the cyclotron viewed from above.
(a) Protons are released from rest at point A and accelerated across the gap between the “dees” by a voltage of 2·00 kV.
Show that the speed of the protons as they first reach the right hand “dee” is 6·19 × 105 m s−1.
(b) Inside the “dees” the electric field strength is zero but there is a uniform magnetic field. This forces the protons to move in semi-circular paths when inside the “dees”.
State the direction of the magnetic field in the “dees”.
(c) While the protons are inside the “dee”, the polarity of the applied voltage is reversed so that the protons are again accelerated when they cross to the left hand “dee”.
Calculate the speed of the protons as they first enter the left hand “dee”.
6.
