A new particle is discovered at Stanford Linear Accelerator.If the total energy of the particle is 17.0 GeV and its momentum is 5.00 GeV/c,what is the rest mass of the particle? A)15.5 GeV/c² B)16.2 GeV/c² C)12.0 GeV/c² D)17.0 GeV/c²

Question

Quizplus · Accepted Answer

We can use the formula for relativistic momentum:

p = γmv

where γ is the Lorentz factor, m is the rest mass, and v is the velocity.

We know that the total energy (E) of the particle is

E = γmc^2 + K

where c is the speed of light and K is the kinetic energy. Since the particle's momentum is non-zero, we know that K is also non-zero, so

E > γmc^2

Solving for γ:

γ = E/(mc^2) > 1

We're given the values of E and p, so we can solve for γ:

γ = E/√(p^2c^2 + m^2c^4)

Squaring both sides:

γ^2 = E^2/(p^2c^2 + m^2c^4)

Rearranging:

m^2c^4 = E^2/γ^2 - p^2c^2

Plugging in the values:

m^2c^4 = (17.0 GeV)^2/(γ^2) - (5.00 GeV/c)^2

Since γ > 1, we know that m < E/c^2. The only answer choice that satisfies that condition is B.

A New Particle Is Discovered at Stanford Linear Accelerator