Intro Nuclear Science v1 - radiochem

```NE 301 - Introduction to Nuclear Science
Spring 2012
Classroom Session 1:
•Homework
#0
•Isotopes and Decay Diagrams
•Nuclear Reactions
•
•
•
Energy of nuclear reactions
Neutron Cross Sections
Activation Calculations
Solution to Homework #0
Please bring clickers to class. We will
start next session to collect points.
Get in pairs, feel free to talk across
tables.
2
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
3
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 amu
REMEMBER: If nothing else is said, masses are natural
isotope mixtures.
4
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?
5
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 collision
Rxn. Rate = N  
6
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?
# of H 2 O M olecules in 1 g = 1 g H 2 O 
6.02e23 m olecules H 2 O
 3.34 e 22
18 g
Density of oxygen atoms:
Density of hydrogen atoms:
What is the density of water molecules in water?
7
5. Cylinder with a diameter and height
of 10 cm weights 15.16 kg. What is it
10 cm
10 cm
8
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 = 5oz
Quad-Lock Unit Converter (or some such)
J W.s
=0.0004 ¢
9
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-h
Or MeV  J  kW-h
How many protons Callaway convert by fission
a day (3,700 MW of installed capacity)?
10
8. The average mass of potassium in
the human body is ~140g. What is
the activity (Bq) of 40K in the body?
A=N.
T1/2=1.27e9 y
The natural abundance of 40K is: 0.0117 %, so N for 40K
N ( nat . K )  140 g 
1 m ole

6.02 e 23 atom s
39.0983 g
 2.16 e 24 atom s
1 m ole
N ( 40 K )  2.16 atom s  0.000117  2.52 e 20 atom s of
A( 40 K )  N .  2.52 e 20 
Ln 2
1.27 e 9 y

1y
365 d

1d
24 h

40
1h
K
 4361.3 Bq
3600 s
11
9.The activity of a radioisotope is found to
decrease by 35% in one week. What are the
values of its:
A A e
(a) decay constant (days-1) 0.7 A  A e
  .t
0
  .1 w eek
0
0
Ln 0.7 =   . 1 w eek
-0.357
 =-
 0.357 w eek
-1
1 w eek
(b) half life (days)
Ln 2
T1 / 2 

0.693
T1 / 2 
(c) mean life(days)?
t
t
0.357 w eek
-1
 1.943 w eeks
1

1
0.357 w eek
-1
 2.804 w eeks
12
11. How many atoms are there in a 1.00 MBq
source of
Na T =15.020 h
(a) 24Na
(b) 238U
24
1/2
A  N
N 
A

1.00 e 6 B q

ln 2

15.020 h
 7.80 e10 atom s
1 h
3600 s
M ( 24 N a )  23.990963 g/m ol
1 m ol
m  7.8 e10 atom s 

23.900963 g
6.02 e 23 atom s
 3.10 e  12 g
1 m ol
= 3.10 pg
238U
T1/2=4.468x109 y
A  N
N 
A

1.0 e 6 B q

ln 2

4.468 e 9 y
1 y
365 d

 2.03 e 23 atom s
1 d
24 h

1h
3600 s
M ( 24 N a )  238.050783 g/m ol
m  2.03 e 23 atom s 
1 m ol
6.02 e 23 atom s

238.050783 g
 80.38 g
1 m ol
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.
13
Nuclear Science
14
Atomic and Nuclear Nomenclature
A
Z
X
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
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Chart of the Nuclides
Isobars
Isotopes
Z
Isotones
N
16
17
Isobars = A
18
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