Question
do question 1 please
A box with dimensions 1m. 2m, 4m is accelerated to speed 0.5c along its longest dimension. Compute the change in its volume. A positron with a kinetic energy of 1MeV (mega electron-volt) collides with an electron at rest. The two particles are annihilated producing two photons. Find the energies of these photons assuming they move along the same direction as the initial positron lone in the same and the other in the opposite direction). A ping pong ball weighs 2.7 grams and can be moving as fast as 60mph midflight. What is the de-Broglie wavelength of such a ball? What is its kinetic energy? You should be able to do well with a non-relativistic approximation here. Now suppose we take the length of a ping pone table L = 274cm as a box and consider the lowest Standing wave that can fit within L on the condition that wave amplitude vanishes at the boundaries (see pic below)-this would be the quantum ground state of the ping pong ball. Compute the ground state energy. What are the wavelength and the energy of the next higher solution (again, the idea is that wave's amplitude must vanish at the walls} =
Explanation / Answer
1. as box is moving 0.5c along its longest dimension.
then this dimension will be L = L0 / Y
Y = 1 / sqrt[1 - (v/c)^2] = 1 / sqrt[1 - .5^2]
Y = 1.155
so L = 4 / 1.155 = 3.464 m
Vo = (1 x 2 x 4) = 8 m^3
V = 1 x 2 x 3.464 = 6.928 m^3
deltaV = Vo - V = 1.072 m^3
