Question

1. ​A negative pion ( ) is a particle that​ ​has a mass equal to 2.49 x 10​-28​ kg. What is the rest π− energy of the pion in joules and in megaelectron-volts (MeV)?

2. ​A negative pion is observed to be moving to the right at 0.950​c ​ .​ ​ What is the negative pion’s total energy (in MeV) ​and ​ momentum at this speed?

3. ​The negative pion decays (splits) into two particles, a muon ( ) and a neutrino ( ). The μ υ muon has a rest energy of 106 MeV, and the neutrino is (virtually) massless. After the decay, the total energy of the neutrino is observed to be 187 MeV. How much total energy must the ​muon ​ have?

4. ​ At what speed is the muon observed to be travelling?

5.  On Earth in 2017, the amount of electrical energy used was 8.03 x 10​16​ J. How much mass would need to be converted directly to energy to release this much energy?

6.  Imagine this conversion of mass to energy all came from nuclear fission reactions of the element uranium. Assume the reaction is 35% efficient: that means that the mass you calculated above to produce the electrical energy is only 35% of the total mass that was converted to energy. The other 65% was “waste” energy. How much total mass was converted to all kinds of energy?

7. The amount of mass actually converted to energy is just a small fraction of the original uranium’s mass: just 0.0000885 of the original mass (0.00885%). Given all these assumptions, how much total mass of uranium must be available to create all the electrical energy used in the world, in one year? (The total reserve of uranium-235 currently available is about 37,000 tonnes, or 3.7 x 10​7​ kg.).

Answer 1