VISUAL PHYSICS ONLINE

8.2 FROM THE UNIVERSE TO THE ATOM

THE NUCLEUS

P82 003

Bubble chambers are used in conjunction with particle accelerators to photographically record the tracks of fast-moving charged particles. An intense magnetic field is applied at right angles to the path of the particles to deflect them according to their charge and momentum. The diagram shows a beam of protons travelling horizontally at 8.00´10⁷ m.s^{-1 and} entering a liquid hydrogen bubble chamber in a vertical magnetic field of 1.82 T. Examination of the photograph taken by the camera, as sketched below, shows that the protons were deflected along a circular path of radius 0.480 m.

q_p = 1.602x10^-19 C m_p = 1.6726x10^-27 kg c = 3.00x10⁸ m.s^-1

(A) Comment on the mass of the accelerated proton.

(B) Derive an expression for the momentum of a proton from the forces it experiences in this experiment.

(C) Calculate the momentum of a proton in the bubble chamber.

(D) Compare the answer in (C) with the relativistic momentum of a proton.

View solution below only after you have completed the answering the question.

Solution

q_p = 1.602x10^-19 C m_p = 1.6726x10^-27 kg c = 3.00x10⁸ m.s^-1

v = 8.00x10⁷ m.s^-1 B = 1.82 T R = 0.35 m q = 90^o

(A)

The modern view in special relativity is that the mass of the proton is a constant and independent of its velocity. It is the momentum of the proton that is now considered to be a function of its velocity.

momentum of proton

(B)

Magnetic force = centripetal force

(C)

Momentum of proton from experiment

(D)

Relativistic momentum

There is a good agreement between the two values of the momentum of the proton.