QUESTION 31 How much energy is released when 0.873 g of uranium-235 (exact mass

Question

QUESTION 31

How much energy is released when 0.873 g of uranium-235 (exact mass = 235.043922 amu) fissions into two neutrons (1.008664916 amu each), strontium-90 (89.907738 amu) and xenon-143 (142.9385 amu). The units are giga-joules where one GJ equals a billion joules (1.0E+9 J). Carry many significant digits in your calculations.

A freshly prepared sample of curium-243 undergoes 3312 disintegrations per second. After 6.00 years, the activity of the sample declines to 2755 disintegrations per second. The half-life of curium-243 is __________ years.

Explanation / Answer

a. Uranium 235 undergo distingeration as;

U235 ---------> Sr90 + Xe143 +2n o

Q= [M(U235 ) - M(Sr90)-M(Xe 143)-2 n o ]c2

Q= [235.043922-(89.907738-142.9385-2*1.008664916)]*931.5 MeV/u

Q= 0.1803541700 *931.5= 167.99990935 Mev

1 gm of Uranium 235 give 167.99990935 Mev of energy

0.873 gm of uranium gives 0.873* 167.99990935 Mev= 146.66392086 MeV

1MeV= 1.6*10^13 J

146.66392086 MeV= 1.6*10^13* 146.66392086/10^9 GJ= 234.66227337*10^4 GJenergy

b. Rate constant k=2.303/t log a/a-x

Here t= 6 years, a= 3312 distingeration per second , a-x= 2755 distingeration per second

Substituting the values, k=2.303/6 log 3312/2755

k= 0.0303 years-1

Half life, t1/2= 0.693/k= 0.693/.0303= 22.87 years

Half life is 22.87 years

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