Physics 4e03 Mt1 2002

Physics 4E03 Test 1 February 15, 2002 (1) The energy of the γ (gamma) ray emitted in the capture of thermal neutrons by hydrogen 1

H + n → 2H + γ

is measured to be 2.2244 Mev. Find the binding energy of the deuteron in Mev. Note: 1 u = 931.5 Mev / c2 (2) From the semi-empirical mass formula, the binding energy per nucleon is

1 A − 2 Z 2 δ pair Z2 B = aV − a S 1 3 − aC 4 3 − a sym ( ) + A A A A A a) briefly define each term in the semi-empirical formula. Give the physical origin (explain the A dependency) of the first three terms. b) Consider nuclei with small nucleon number A and such that Z = N = A/2. Neglecting the pairing term, show that the binding energy per nucleon will change to: 1

2

− B = aV − aS A 3 − ( aC 4) A 3 . A

c)

At What Z does the above expression reach a maximum.

d) Using the changed mass formula, compute the atomic mass of the nuclide of part c. The constants are: aV = 15.5 Mev, aS = 16.8 Mev, aC = 0.72 Mev and asystem = 23 Mev. 13 6

(3) We will study the reaction

C + 136 C → 1226Mg *

Both identical fermions are in the ground state in the entrance channel and the initial orbital angular momentum is

li ≤ 2. The ground state of

and an angular momentum of 1 . Deduce all the possible 2

in

26

Mg .

13 6

C has a negative parity

I π values for the populated

(4) Write the properties of the short range strong nuclear force. Explain each of them in a very brief but precise way.

symbol n 1 H 2 H

Atomic mass Z 0 1 1

Mass (u) 1.00866501 1.007825 2.014102

Useful note:

E γ = pγ c For quadratic equation: ax + bx + c = 0 2

⇒ END

x=

− b + b 2 + 4ac 2a