1. ​A negative pion ( ) is a particle that​ ​has a mass equal to2.49 x 10​-28​ kg. What is the rest π− energy of the pion in joulesand in megaelectron-volts (MeV)?

2. ​A negative pion is observed to be moving to the right at0.950​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, thetotal energy of the neutrino is observed to be 187 MeV. How muchtotal 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 energyused was 8.03 x 10​16​ J. How much mass would need to be converteddirectly to energy to release this much energy?

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

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