Nuclear Physics, JU, Second Semester, 2010-2011 (Saed Dababneh). 1 Radioactivity.

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Nuclear Physics, JU, Second Semester, (Saed Dababneh). 1 Radioactivity

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 2 Radioactivity

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 3 Radioactivity Natural decay series Other 2? HW 10

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 4 Radioactivity

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 5 Radioactivity

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 6 Radioactivity ≡ decay constant. Compare to human life time!!!

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 7 Show that the mean lifetime. N is difficult to measure. Instead, measure  N ≡ number of decays between t and t +  t :  t <<  (i.e. << t 1/2 ) If  t <<  (i.e. << t 1/2 ) then show that and thus defining the activity A(t ): RadioactivitySlope=?!!!!!!!!!! Be careful.

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 8 Radioactivity HW 11 Krane Problem 6.1 Activity measured in units of becquerel (Bq) = 1 decay/s. 1 curie (Ci) = 3.7 x Bq. Activity is not dose!!!!!

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 9 Radioactivity Exponential decay of species 1 and exponential growth of species 2. Isotope 1 (initial number N 0 ) decays into “stable” isotope 2.

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 10 Radioactivity If parent nucleus decays by two modes: Derive.

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 11 Radioactivity If radioactive species 1 is produced in a reactor or accelerator with rate R. ProductionDecay Show that and thus secular equilibrium almost linear HW 12

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 12 Radioactivity How long should we irradiate? Activity per cost?

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 13 Radioactivity If species 2 is radioactive. Possible also that species 3 is radioactive. 1  2  3  4 ….. until we reach a stable isotope. But for now let us consider species 3 to be stable. For the parent nucleus assume that N 1 (t=0)=N 0. For the daughters assume that N 2 (t=0) = N 3 (t=0) = 0. Verify the following: What if 2 = 0? What if 1 is very small? N 1 ( t ) = ?

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 14 Secular equilibrium 1 is very small ( 1 << 2 ) ► For large time t, A 2  N 0 1 which is the limiting value for secular equilibrium. Constant activity ► production = decay. Radioactivity ▼ What if t ½ for 132 Te were 78d?

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 15 Radioactivity Transient equilibrium If 1 is smaller than 2 ( 1 < 2 ), show that

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 16 Radioactivity As t increases, but the activities themselves are not constant. 230 Th decays, in effect, with the decay constant of 234 U. Parallel !?

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 17 Radioactivity Discuss the case when 1 is larger than 2 ( 1 > 2 ).

Nuclear Physics, JU, Second Semester, (Saed Dababneh). 18 Radioactivity In general, 1  2  3  4 ….. until we reach a stable isotope. If N 0 of type 1 and N 2 (t=0) = N 3 (t=0) = … = 0 ► Bateman equations. Exclude the term ( k - k ).