33.4 Particles, patterns, and conservation laws  (Page 7/22)

Large quantities of antimatter isolated from normal matter should behave exactly like normal matter. An antiatom, for example, composed of positrons, antiprotons, and antineutrons should have the same atomic spectrum as its matter counterpart. Would you be able to tell it is antimatter by its emission of antiphotons? Explain briefly.

Massless particles are not only neutral, they are chargeless (unlike the neutron). Why is this so?

Massless particles must travel at the speed of light, while others cannot reach this speed. Why are all massless particles stable? If evidence is found that neutrinos spontaneously decay into other particles, would this imply they have mass?

When a star erupts in a supernova explosion, huge numbers of electron neutrinos are formed in nuclear reactions. Such neutrinos from the 1987A supernova in the relatively nearby Magellanic Cloud were observed within hours of the initial brightening, indicating they traveled to earth at approximately the speed of light. Explain how this data can be used to set an upper limit on the mass of the neutrino, noting that if the mass is small the neutrinos could travel very close to the speed of light and have a reasonable energy (on the order of MeV).

Theorists have had spectacular success in predicting previously unknown particles. Considering past theoretical triumphs, why should we bother to perform experiments?

What lifetime do you expect for an antineutron isolated from normal matter?

Why does the ${\eta }^0$ meson have such a short lifetime compared to most other mesons?

(a) Is a hadron always a baryon?

(b) Is a baryon always a hadron?

(c) Can an unstable baryon decay into a meson, leaving no other baryon?

Explain how conservation of baryon number is responsible for conservation of total atomic mass (total number of nucleons) in nuclear decay and reactions.

The ${\pi }^0$ is its own antiparticle and decays in the following manner: ${\pi }^0\to \gamma +\gamma$ . What is the energy of each $\gamma$ ray if the ${\pi }^0$ is at rest when it decays?

The primary decay mode for the negative pion is ${\pi }^{-}\to {\mu }^{-}+{\stackrel{-}{\nu }}_{\mu }$ . What is the energy release in MeV in this decay?

The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is ${\text{10}}^{\text{14}}\text{GeV/}{c}^2$ .

(a) How many proton masses is this?

(b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity $\gamma$ would have to be.)

The decay mode of the negative muon is ${\mu }^{-}\to e^{-}+{\stackrel{-}{\nu }}_e+{\nu }_{\mu }$ .

(a) Find the energy released in MeV.

(b) Verify that charge and lepton family numbers are conserved.

The decay mode of the positive tau is ${\tau }^{+}\to {\mu }^{+}+{\nu }_{\mu }+{\stackrel{-}{\nu }}_{\tau }$ .

(a) What energy is released?

(b) Verify that charge and lepton family numbers are conserved.

(c) The ${\tau }^{+}$ is the antiparticle of the ${\tau }^{-}$ .Verify that all the decay products of the ${\tau }^{+}$ are the antiparticles of those in the decay of the ${\tau }^{-}$ given in the text.

The principal decay mode of the sigma zero is ${\text{Σ}}^0\to {\text{Λ}}^0+\gamma$ .

(a) What energy is released?

(b) Considering the quark structure of the two baryons, does it appear that the ${\text{Σ}}^0$ is an excited state of the ${\text{Λ}}^0$ ?

(c) Verify that strangeness, charge, and baryon number are conserved in the decay.

(d) Considering the preceding and the short lifetime, can the weak force be responsible? State why or why not.

(a) What is the uncertainty in the energy released in the decay of a ${\pi }^0$ due to its short lifetime?

(b) What fraction of the decay energy is this, noting that the decay mode is ${\pi }^0\to \gamma +\gamma$ (so that all the ${\pi }^0$ mass is destroyed)?

(a) What is the uncertainty in the energy released in the decay of a ${\tau }^{-}$ due to its short lifetime?

(b) Is the uncertainty in this energy greater than or less than the uncertainty in the mass of the tau neutrino? Discuss the source of the uncertainty.