Nuclear & Particle Physics - Standard Model

According to the Standard Model of elementary particles, which of the following is NOT a composite object?

A. Muon
B. Pi-meson
C. Neutron
D. Deuteron
E. Alpha particle

(GR9677 #63)

Solution:

A.TRUE
Muon is a lepton. Leptons, along with quarks, are considered the fundamental particles.

B. FALSE
Pi-Meson consists of a quark and its antiparticle. Moreover, a pi-meson is a hadron. Hadrons interact with the strong-force, and all of them are composed of combinations of quarks. (The fundamental particles are classified as quarks and leptons.)

C. FALSE
A neutron is made up of 3 quarks.

D. FALSE
A deuteron consists of a proton and a neutron. (tritium is two neutrons and a proton, while regular Hydrogen is just an electron and proton).

E. FALSE
An alpha particle consists of electrons and protons and neutrons.

Answer: A

Special Relativity - Time Dilation

Tau leptons are observed to have an average half-life of Δt₁ in the frame S₁ in which the leptons are at rest. In an inertial frame S₂, which is moving at a speed v₁₂ relative to S₁, the leptons are observed to have an average half-life of Δt₂. In another inertial reference frame S₃, which is moving at a speed v₁₃ relative to S₁ and v₂₃ relative to S₂, the leptons have an observed half-life of Δt₃. Which of the following is a correct relationship among two of the half lives, Δt₁, Δt₂, and Δt₃.

A.

B.

C.

D.

E.

(GR9277 #38)

Solution:

Time Dilation:

Δt_j =  γ_ijΔt_i



Δt_i = time in a rest frame
Δt_j = time in a moving frame

In this problem, Δt₁ = time in a rest frame
Time dilation only relates to time in a rest frame Δt₁ with time in a moving frame, Δt₂ or Δt₃

The only right answers:
Δt₂ =  γ₁₂Δt₁
Δt₃ =  γ₁₃Δt₁

(C) and (D) are FALSE (no Δt₁ in the equation)
(E) is FALSE (relates v₂₃ with Δt₁ and Δt₂)

(A) FALSE
Δt₂ = Δt₁ [1 − (v₁₂)²/c²]^½ = Δt₁ (1/γ₁₂) → Δt₁ = γ₁₂Δt₂ 

(B) TRUE
Δt₁ = Δt₃ [1 − (v₁₃)²/c²]^½ = Δt₃ (1/γ₁₃) → Δt₃ = γ₁₃Δt₁ 

Answer: B