# hwk10 - just use a number of the right order of magnitude...

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Physics 31: Homework #10 Due Thursday, April 10, 2008 Problem A: A particle of mass m moves in a three dimensional box of unequal sides L 1 , L 2 ,and L 3 . Find the energies of the six lowest states if L 1 = L , L 2 =2 L ,and L 3 =3 L . Which of these states are degenerate (have the same energy)? Problem B: Radium ( 226 88 Ra) decays by α emission to radon ( 222 86 Rn). The energy of the emitted α particle is E =4 . 78 MeV. Estimate the number of times per second that the alpha particle strikes the nuclear boundary. ( Hint: You will need to estimate the nuclear radius;
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Unformatted text preview: just use a number of the right order of magnitude.) Estimate the half life of 226 88 Ra. Problem C: A Geiger counter is used to measure the radioactive decay of a sample of an unstable isotope. If the count rate is 100 per minute at a given time and 90 per minute exactly one week later, what is the half life of the isotope? Problem D: Show that 1 r 2 d dr " r 2 d dr Ã ψ ( r ) r !# = 1 r d 2 ψ dr 2 . No problems from Beiser this week....
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