NE 301 - Introduction to Nuclear ScienceSpring 2012

Classroom Session 1:

•Homework #0•Radioactive Types•Radioactive Decay and Growth•Isotopes and Decay Diagrams•Nuclear Reactions

• Energy of nuclear reactions• Neutron Cross Sections• Activation Calculations

2

Solution to Homework #0

Please bring clickers to class. We will start next session to collect points.

Please bring calculators.

Get in pairs, feel free to talk across tables.

Time on task please. I want everybody working to get answers.

3

1. What is atomic and molecular weight? What is the difference between the two concepts?

Weight of an atom vs. weight of a molecule.

Both can be given in:

AMU or grams/mole

4

Example:What is the molecular mass of Uranil Sulfate (UO2SO4)?

M(UO2SO4)= MU+6*MO+MS

M(UO2SO4)= MU+6*MO+MS =

= 238.029 g/mol + 6* 15.999 g/mol + 32.066

M(UO2SO4) = 366.089 g/mol or amuREMEMBER: If nothing else is said, masses are natural isotope mixtures.

5

2. Define the Avogadro’s number according to your own understanding.

Think of a dozen, but 6.022e23 instead.

What is the weight of a mol of H2 molecules?

What is the weight of a mol of H

atoms?

What is the weight of a mol of electrons?

6

3. Explain the difference between mass density () and atom density (N)

= m / V

N = # atoms / V

Why atomic density is important in nuclear engineering?

Nuclear reactions are a collisionRxn. Rate = N

7

4. What is the atom density of oxygen in water? ( = 1 g/cm3, M = 18 g/mol). What is the atom density of hydrogen in water?

22 2

6.02e23 molecules H O# of H O Molecules in 1 g = 1 g H O 3.34 22

18 ge

Density of oxygen atoms:

Density of hydrogen atoms:

What is the density of water molecules in water?

8

5. Cylinder with a diameter and height of 10 cm weights 15.16 kg. What is it likely made out of?

Google it!

10 cm

10 cm

9

6. What is the classical formula for kinetic energy? How much kinetic energy has a baseball traveling at 100mph in Joules? How much would it cost to buy that amount of electrical energy (assume 10¢/kW-h)

Google mass of baseball = 5ozQuad-Lock Unit Converter (or some such)

=0.0004 ¢

J W.s

10

7. How much energy in Joules is there in a proton if we could convert it entirely in energy using Einstein equation (E=mc2)? How much is that in KW-h?

Either kg mc2 J kW-hOr MeV J kW-h

How many protons Callaway convert by fission a day (3,700 MW of installed capacity)?

11

8. The average mass of potassium in the human body is ~140g. What is the activity (Bq) of 40K in the body?

40

( . )

40

( )

1 mole 6.02 23 atoms140 2.16 24

39.0983 1 mole

2.16 0.000117 2.52 20 atoms of

nat K

K

eN g e atoms

g

N atoms e K

40( )

Ln 2 1 1 1. 2.52 20 4361.3 Bq

1.27 9 365 24 3600K

y d hA N e

e y d h s

A=N.

T1/2=1.27e9 y

The natural abundance of 40K is: 0.0117 %, so N for 40K

12

9.The activity of a radioisotope is found to decrease by 35% in one week. What are the values of its:(a) decay constant (days-1)

(b) half life (days)

(c) mean life(days)?

.0

00.7

tA A e

A

0A .1 week

-1

Ln 0.7 = . 1 week

-0.357=- 0.357 week

1 week

e

1/ 2

1/ 2 -1

Ln 2

0.6931.943 weeks

0.357 week

T

T

-1

1

12.804 weeks

0.357 week

t

t

13

11. How many atoms are there in a 1.00 MBq source of (a) 24Na (b) 238U 1.00 6 Bq

ln 2

15.020 h

A N

A eN

1 h

3600 s

7.80 10 atomse

24( )23.990963 g/mol

1 mol 23.900963 g7.8 10 atoms 3.10 12 g

6.02 23 atoms 1 mol = 3.10 pg

NaM

m e ee

1.0 6 Bq

ln 2

4.468 9 y

A N

A eN

e

1 y

365 d

1 d24 h

1h3600 s

2.03 23 atomse

24( )238.050783 g/mol

1 mol 238.050783 g2.03 23 atoms 80.38 g

6.02 23 atoms 1 mol

NaM

m ee

Notice that equally active sources can have vastly different masses (14 orders of magnitude) depending on half-life. Short-lived isotopes are a lot more active than long-lived ones.

24Na T1/2=15.020 h

238U T1/2=4.468x109 y

14

Nuclear Science

15

Atomic and Nuclear Nomenclature

X element symbol (H, He, Na, Xe, U, etc.) represents the number of charges in the nucleus (thus electrons, thus chemical behavior).

A = Mass number = protons + neutrons = Nucleons.

Z = atomic number = protons. X and Z are redundant and normally we only

write AX.

e.g. 235U, 16O, 3H, 14C

ZAX

16

Chart of the Nuclides

Z

N

Isobars

Isotopes

Isotones

17

18

Isobars = A