An electron and a proton are each accelerated through a potential difference of 10.0 million volts.

a) What is the kinetic energy of the electron? What is the kinetic energy of the proton?
b) Calculate the momentum (MeV/c) of the proton using classical equations.
c) Calculate the momentum (MeV/c) of the proton using relativistic equations.
d) Calculate the momentum (MeV/c) of the electron using classical equations.
e) Calculate the momentum (MeV/c) of the electron using relativistic equations.
f) Why is there a difference?

Solution Preview

a) The kinetic energies of both the proton and the electron are 10.0 MeV since they each have a charge of +/-e.

b) The classical momentum P_c of the proton is given by

Prove that the De Broglie wavelength associated with a particle having kineticenergy K which is not negligible compared to its rest energy m_0 c^2 is given by
lemda = [h/(m_0 K)^(1/2)](1 + K/2m_0 c^2)^(-1/2)
The complete solution is in the attached file.

9-The Tevatron accelerator at the Fermi National Accelerator Laboratory (Fermilab) outside Chicago actually consists of 5 stages to sequentially boost protons to 1 TeV (1000 GeV). What is the speed of the proton at the end of each stage? Note: the numbers given in parentheses represent the total kineticenergy at the end of each

A 0.4kg ball moving with speed of 3m/sec collides with a 0.6kg mass initially at rest. If the two particles stick together during the collision, find the momentum, velocity, andkineticenergy of the system after the collision.

A 0.343 kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with one half the original speed of the first ball. 1) What is the mass of the second ball? And 2) what fraction of the original kineticenergy gets transferred to the second ball?

Part 1
Suppose optical radiation (of wavelength 2.6 × 10^-7 m) is used to determine the position of an electron to within the wavelength of the light. The mass of an electron is 9.10939 × 10^-31 kg and the Planck's constant is 6.62607 × 10^-34 J · s.
What will be the minimum resulting uncertainty in the electron's velocit

1) A 10.0 g moving to the right at 20.0 cm/s makes and elastic head on collision with a 15.0 g object moving in the opposite direction at 30.0 cm/s. Find the velocity of each object after collision.
2) a 90 kg fullback moving east with a speed of 5 m/s is tackled by a 95 kg opponent running north at
3.0 m/s. If the collis

A particle of mass 3.5 MeV/c2 andkineticenergy 4.5 MeV collides with a stationary particle of mass 0.5 MeV/c2 . After the collision, the particles stick together.
(part 1 of 5)
Find the total energy of the first particle before the collision. Answer in units of MeV.
(part 2 of 5)
Find the speed of the first particl

For this question you need to know that an electron accelerated through an electric potential difference of V volts acquires a kineticenergy of V eV. (This question is best done by not converting to joules, but by exploiting the fact that mec2 is given as 0.511 MeV).
i)
What is v/c for an electron?
a) Striking the screen