Nuclear Reactions Questions

1. Pu-239 (nuclear mass of 239.0006 amu) decays by alpha emission to U-235 (nuclear mass of 234.9934). Calculate how much energy is given off by the decay of 2.00 mg of Pu-239.

239/94 Pu = 235/92 U + 4/2 He

defect of mass for one atom is $m =239.0006-234.9934-4.0026 = 0.0046 amu =$

$=0.0046*1.66*10^{-27} = 7.636*10^{-30} kg$

kg Pu ……..$6.022*10^{23}$ atoms

mg Pu………….x atoms

$x =2*10^{-6}*6.022*10^{23}/239 =1.2*10^{18}$ atoms

The total energy released is (c is the speed of light)

$E =x*defect of mass*c^2 =1.2*10^{18}*6.39*10^{-38}*(3*10^8)^2 =6.9*10^{-3}$ J　

2. What is the mass defect of K-40 (nuclear mass of 39.95358)?

there are 19 protons (mass =1.007 3 amu) and 21 neutrons (mass =1.00866 amu)

mass defect is $19*1.0073 + 21*1.00866 -39.95358 =0.36698 amu = 6.09*10^{-28}$ kg

3. What is the binding energy of K-40?

Total binding energy (in Mev) is (A is the atomic mass, Z is the number of protons)

$B(A, Z) =15.36*A -16.32*A^{(2/3)} -90.45*(A/2 -Z)^2/A -0.6928*Z^2/A^{(1/3)}$　

$B(40,19) =614.4 – 193.24 – 2.26 – 73.22 = 345.68 MeV$

4. Food can be preserved by radiation with gamma rays. A y-ray source has an activity of 575 Ci.

How many disintegration are there per minute?

$1 Curie =3.7*10^{10} Bq =37 GBq =37*10^9$ disintegration/sec

$575 Ci =575*37*10^9$ disintegration/sec $= 21275*10^9$ disintegration/sec = $1.2765*10^{15}$ disintegration/minute

lodine-131 has a half-life of 8.1 days. This isotope decays by beta particle emission.

5. Write a balanced nuclear equation for the decay of iodine-131.

(131/53) I = (0/-1)electron (or beta particle) + neutrino + (131/54) Xe + (0/0) gamma + 970 KeV

6. What is the activity (in Curies) of a 2.50 mg sample of the isotope (atomic mass= 126.9 amu)?

The activity A is $A =\lambda*N$

where lambda is the decay constant and N is the total number of nucleus

$\lambda = ln(2)/T(1/2)$

where T(1/2 )is the half time life

$T(1/2) =8.1 days =8.1*24*3600 =7*10^5$ seconds

$\lambda = ln(20/7*10^5 = 9.9*10^{-7}$

.9 Kg …………….$6.022*10^{23}$ nucleus

$.5*10^{-6}$ kg ………..x nucleus

$x =2.5*10^{-6}*6.022*10^{23}/126.9 =1.186*10^{16}$ nucleus

$Activity = x*\lambda =1.186*10^{16} *9.9*10^{-7} = 1.175*10^{10}$ disintegration/second $=1.175*10^{10} Bq = 0.317 Curie$

Th-230 decays by alpha emission.

7. Calculate m in grams when one mole of Th-230 decays.

mass of (230)Th = 230 amu

amu means 230 grams/mole hence in one mole the mass is 230 grams

8. Calculate E in kilojoules when one gram of 230Th decays.

$(232/90) Th = (4/2) \alpha + (228/88) Ra +4.08 MeV$

$(228/90) Th = (4/2) \alpha + (224/88) Ra +5.52 MeV$

the average decay energy per one atoms of (230) Th is (4.08+5.52)/2 =4.80 MeV

kg Th ………………….$6.022*10^{23}$ atoms

g Th ………………………..x atoms

$x =2.618*10^{18} atoms

The total energy is $E =x*decay energy =4.8*2.618*10^{18} =1.257*10^{19}$ MeV $=1.257*10^{19}*1.6*10^{-19}*10^6 = 2*10^6$ Joule

Write the formula for each of the following:

9. an alkyne with 10 hydrogen atoms

C10H10

10. an alkene with 22 hydrogen atoms

C11H22

11. an alkane with 8 carbon atoms

C3H8

Give the structure of each of the following: (Draw all C & H atoms as well as functional groups.)

12. a two-carbon alcohol

C2H5(OH) = (CH3)-(CH2)-(OH)

13. an ether with three carbons

CH3-CH2-O-CH3

14. an aldehyde with two carbons　

CH3-CHO