NE 105 - Introduction to Nuclear EngineeringSpring 2011

Classroom Session 3 - Fundamental Concepts

•Molecular weight•Mole•Isotopic Abundances•Classic and Relativistic Calculations•Photon Interactions with Matter

2

Chart of the Nuclides

Z

N

Isobars

Isotopes

Isotones

3

Atomic Mass Unit

1/12 of the mass of 12C Units are: AMU (1 AMU= 1.66e-27 kg) or g/mole How much a Mole of something weights

Mole (mol) = Avogadro # of entities. Atomic and molecular weights are given in

grams/mole Concept similar to a “dozen” except it is:

6.022 x 1023

6.02e23 atoms of carbon weight 12 g

Notice the mole concept let you convert from mass to number of atoms/molecules

4

What is the atom density of hydrogen in liquid water (H2O)? = 1 g/cm3, MO = 16 g/mol and MH = 1 g/mol

6.7

e22

at./c

m3

2 a

t./cm

3

6.7

e16

at./c

m3

6.7

x102

2 cm

-3

2 g

/cm

3

20% 20% 20%20%20%

1. 6.7e22 at./cm3

2. 2 at./cm3

3. 6.7e16 at./cm3

4. 6.7x1022 cm-3

5. 2 g/cm3

5

3

g 1 mole H2O 6.02 23 molecules H2O 2 atoms H1

cm 18 g 1 mole H2O 1 molecule H2O

e

6.7e22 H atoms/cm3 (1 and 4 are correct)

6

Notice equation for atomic density is:

aNAcmatN

)/.( 3

Advice: Work the units Think of the concepts In case of isotopes remember to use abundances (i)

NOTICE: To find A (molecular weight) of a mixture we need to take

into account the composition of it as well. The periodic table presents the molecular weight of the

“natural” mix of isotopes ONLY.

It is better to use “understanding“ instead of the equation

7

What is the 235U atom density in 3% enriched U fuel? (UO2=10.50 g/cm3)

7.0

2e20

at./

cm...

2 a

t./cm

3

6.7

e16

at./c

m3

7.0

2x10

20 c

m-3

2 g

/cm

3

20% 20% 20%20%20%

Reminder: Enrichments are usually given in atom % (table C.1), assume only 238U and 235U

1. 7.02e20 at./cm3

2. 2 at./cm3

3. 6.7e16 at./cm3

4. 7.02x1020 cm-3

5. 2 g/cm3

8

What is the 235U atom density of 3% enriched 235U fuel? (UO2=10.50 g/cm3)

2382

2352

23523%

3

a U-238 molecule weights: 238.05 2 16 270.05

a U-235 molecule weights: 235.04 2 16 267.04

in the mix 97% is U-238 and 3% U-235:

0.97 270.05 0.03 267.04 269.96

1 molg10.50

cm

UO

UO

UO

M

M

M

2

23

2

235

U-235 3 3

3%

e UO 6.022e23 molecules 1 U atom U atoms2.34 22

269.96 g 1 mole UO 1 molecule cm

U atoms U atomsN =0.03 2.34 22 7.02 20

cm cmNotice it is the same as: 238.05*0.97 235.04*0.03 2 16 269.96UO

e

e e

M

9

What if we use wrong M? What is the atom density of 3% enriched 235U

fuel? (UO2=10.5 g/cm3)238

2

2352

23 3

2

23

238.05 2 16 270.05

235.04 2 16 267.04

1 mole UOg 6.022e23 molecules 1 U atom U atoms10.50 2.34 22

cm 270.05 g 1 mole UO 1 molecule cm

1 mole UOg 6.022e23 molecules10.50

cm 267.04 g 1 mo

UO

UO

M

M

e

2382

32

1 U atom U atoms2.37 22

le UO 1 molecule cm

2.34 2.37Error of using 100 1.12%

2.34UO

e

M

10

Electron Volt

Work done by one electron accelerated through a potential difference of one volt

1 eV = 1.60217646x10-19 J

Example:What is the speed (m/s) of a 12 eV 134Xe

ion?(from the chart of the nuclides: 134Xe Weights = 133.905394

AMU)Use classic concept of KE for nowamu in table 1.5Joule = Energy, Work = Force (N) x d =kg m2/s2

11

Correction of the book… REMEMBER!

Please ignore the c2. It is confusing

Book: Page 6

12

4156.4 m/s ~9,300 m.p.hi.e. even very low energy ions are moving pretty fast

Please remember this is ONLY for classical calculations.At energies close to “c”, need to use relativistic calculations