Question

Part1. Calculate the nuclear binding energy (in J) and the nuclear binding energy per nucleon of

241	Pu
94

(241.0568453 amu).

Part 2.

A freshly isolated sample of ⁹⁰Y was found to have an activity of 8.2 × 10⁵ disintegrations per minute at 1:00 p.m. on December 3, 2006. At 2:15 p.m. on December 17, 2006, its activity was measured again and found to be 2.2 × 10⁴ disintegrations per minute. Calculate the half-life of ⁹⁰Y.

Answer 1

1) First we find mass defect = ( theoretically calculated mass) - experimentally observed mass

241 Pu has 94 p ( protons) and 241-94 = 147 n ( neutrons)

theoretical mass = numper of p x mass of p + number of n x mass of n

                  = 94 x ( 1.0072766) + ( 147 x 1.0086654)

                  = 242.957814 amu

mass defect = 242.957814 - 241.0568453 = 1.909689 amu = 1.909689 x 1.6605388 x 10^ -27 kg

             = 3.15663 x 10^ -27 kg

Binding enegy = mass defect x speed of light ^2 /

                                 = ( 3.1566x10^ -27 x (3x10^8)^2

                             = 2.84 x 10^ -10 J

Binding energy per nucloen = ( 2.84x10^ -10 ) /241 = 1.179 x 10^ -11 J/nucleon

2) radio active deca followst 1st order kinetcis

k = ( 1/t) ln ( a/a-x) where a = 8.2x10^5 , a-x = 2.2x10^4 ,

t = time = dec 17 2.15 pm - dec 3 1pm = 14 days + 1hr + 15 min = ( 14 x 24x60) min + 60 min + 15 min

      = 20235 min

now k = ( 1/20235) ln ( 8.2x10^5) / ( 2.2x10^4)

   = 0.000178812

half life = ln 2/ k = ln 2 / ( 0.000178812) = 3876.4 min