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The muon (mu) is a subatomic particle of the lepton family which has same charge and magnetic behavioue as the electron, but has a different mass and is unstable, i.e. it disintegrates into other particles within microseconds after its creation. Here you will attempt to determine the mass of the muon using two rather different approaches. (a) the most common spontaneous disintegration reaction for the muon is: mu rarr e+bar(v)_(e)+v mu where bar(v)_(e) is the electron antineutrino and v_(mu) the muon neutrino. In a given experiment using a stationary muon, bar(v)_(e)+v mu, carried away a total energy of 2.000xx10^(-12) J, while the electron was moveing with a kinetic energy of 1.4846xx10^(-11) J. Determine the mass of the muon. (b) Many experiments have studied the spectroscopy of atoms that have captured a muon in place of an electron. These exotic atoms are formed in a variety of excited states. The transition from the third excited state to the first excited state of an atom consisiting of a ^(1)H nucleus and a muon attached it was observed at a wavelength of 2.615 nm. Determine the mass of the muon. |
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Answer» `E_(mu)=m muc^(2)E_(E)+E_(V .V)` `m_(mu)c^(2)=m_(e)c^(2)+(T_(e)+E_(v. v))` `m_(mu)=(Me+(T_(e)+e_(V.V)))/(C^(2))=(9.109xx10^(-31)+(1.4846xx10^(-11)+2.000xx10^(-12)))/((2.998xx10^(8))^(2))` `=1.883xx10^(-23) kg` {:b) From Bohr theory: `E_(n)=(me^(4))/(2n^(2)h^(2))=-109700 cm^(-)xx1/n^(2)xx(m/m_(e))` `m=(m_(mu)m_(H))/(m_(mu)+m_(H))` `lambda=(1)/(E_(4)-E_(2))=(1)/(109700(m/m_(e))(1/4-1/16))=2.615xx10^(-7) cm` `m/m_(e)=185.9` `m=185.9xx9.109xx10^(-31)=1.693xx10^(-28) kg` The mass of a proton from Tables ATTACHED `m_(H)=1.673xx10^(-27) kg` `m_(mu)=(mm_(H))/(m_(H)-m)=(1.693xx10^(-28)xx1.673xx10^(-27))/(1.673xx10^(-27)-1.693xx10^(-28))=1.884xx10^(-28) kg` |
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