{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

This preview shows pages 1–6. Sign up to view the full content.

1 Lecture 4 : Beta stability, the LD Mass Formula, and Accelerators Simplest form of LD Mass Formula TBE = C 1 A C 2 A 2/3 C 3 Z 2 /A 1/3 C 4 (N-Z) 2 /A 2 + C 6 /A 1/2 <BE> = C 1 C 2 A 1/3 C 3 Z 2 /A 4/3 C 4 (N-Z) 2 /A 3 + C 6 /A 3/2 E. Line of Beta Stability – Isobars 1. Beta Decay – Form of Radioactive Decay n p conversion inside nucleus A doesn't change; just N/Z ratio ISO BARS Most probable N/Z ratio Line of Beta Stability 2. Example: A = 75 chain 30 75 Zn 31 75 Ga 32 75 Ge 33 75 As 34 75 Se 35 75 Br 36 75 Kr 3. Isobaric Mass Formula Since in decay the mass number remains constant, it is useful to develop an isobaric mass formula (“iso” means same in Greek). A is constant in Binding Energy Equation ( & <BE> form) Z A X = Z H + N n TBE plug in LD Mass Equation Z A X = d 1 Z 2 + d 2 Z d 3 + d + d 4 , where d i = f (Ci, A) This is equation for a parabola; minimum defines most stable nuclide for a given A. These values define the "valley of stability". Atomic number of this nucleus is Z A . Beta- Stable Nucleus n p n p N/Z= 1.08 N/Z= 1.5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Two Cases a. Case I: odd-A nuclei ( = 0) Single parabola: Z A X = d 1 Z 2 + d 2 Z + d 3 ; one Parabola Most probable charge: ( Z A X Z ) = 2d 1 Z A + d 2 A=125 mass parabola RESULT: ONE STABLE ISOTOPE PER MASS NUMBER M(Z)-M(Z A ) in MeV Z
3 Consider the two mass parabolas of A=75 and A=157. What do you notice?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 b. Case II: even A nuclei ( = 1) ( 2 A X ) = d 1 Z 2 + d 2 Z + d 3 d 4 RESULT: Two parabolae ; even-Z always lower CAN HAVE 1, 2 OR 3 STABLE NUCLEI PER A A=128 Upper parabola is odd-odd; Lower parabola is even-even.