Modern Physics: Mastering Physics: ± Creating a Particle

Sunday, January 30, 2011

Mastering Physics: ± Creating a Particle

Two protons (each with rest mass $m =1.67 \times 10^{-27}\;{\rm kg}$ ) are initially moving with equal speeds in opposite directions. The protons continue to exist after a collision that produces an $\eta^{0}$ particle. The rest mass of the $\eta^{0}$ is $m_\eta=9.75 \times 10^{-28}\;{\rm kg}$ .

Part A

If the two protons and the $\eta^{0}$ are all at rest after the collision, find the initial speed

of the protons.

Express your answer as a fraction of the speed of light to three significant figures.

ANSWER:

=

0.6331

Part B
What is the kinetic energy of each proton?

Express your answer in millions of electron volts to three significant figures.

ANSWER:

E_k

=

273.7

$\rm MeV$

Part C
What is the rest energy of the $\eta ^{0}$ ?

Express your answer in millions of electron volts to three significant figures.

ANSWER:

E_r

=

547.3

$\rm MeV$

Notice that the rest energy of the $\eta^{0}$ is equal to the total kinetic energy of the two protons, as expected from the conservation of energy.

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