No Slide Title · Atoms are composed of PROTONS NEUTRONS ELECTRONS + positively charged mass = 1.6726 x 10–27 kg neutral mass = 1.6750 x 10–27 kg negatively charged – • mass

Nuclear Chemistry

Atoms are composed of

PROTONS

NEUTRONS

ELECTRONS

positively charged mass = 1.6726 x 10–27 kg+

neutral mass = 1.6750 x 10–27 kg

negatively charged–• mass = 9.1096 x 10–31 kg

the Nucleus

+

+

made up of protons and neutrons

Nuclear Force

+

+

the neutrons within the nucleus act as sort of glue countering the electrostatic repulsion between the protons

when an unstable nuclei increases its stability by altering its number of neutrons and protons

Radioactivity

Types of Nuclear Decay

Alpha emission ( α)42

0 -1Beta emission ( β )

Electron capture ( e) 0 -1

Positron emission ( β ) 0 +1

Gamma emission ( γ)00

Alpha emission ( α)42

the nucleus emits a helium nuclei ( 2 protons and 2 neutrons

α42 = 4

2 He

Po Pb +210 20684 82

42 He

Beta emission ( β )the nucleus changes a neutron into a proton by emitting an electron

0 -1

β 0 -1

10

n 1 1

p+

C +146

147 Nβ 0

-1

Positron emission ( β )the nucleus changes a proton into a neutron by emitting a positron

0 +1

β 0 +1

11

p 1 0

n+

B +85

84 Beβ 0

+1

Electron capture ( e )the nucleus captures an electron and changes a proton into a neutron

0

β 0 -1

11

p 1 0

n+

-1

C116

11

5 Bβ 0 -1 +

electromagnetic radiation emitted during nuclear decay

Gamma emission ( γ )00

Po Pb +210 20684 82 X

Cs Ba +137 13755 56

Na Ba +20 2011 10

X

X

balance the following nuclear equations

Po Pb +210 20684 82

42 He

Cs Ba +137 13755 56

Na Ba +20 2011 10

X

X

balance the following nuclear equations

Po Pb +210 20684 82

42 He

Cs Ba +137 13755 56

Na Ne +20 2011 10 X

0-1β

balance the following nuclear equations

Po Pb +210 20684 82

42 He

Cs Ba +137 13755 56

Na Ne +20 2011 10

0-1β

0+1β

balance the following nuclear equations

Nuclear Stability

the principle factor in determining whether a nucleus is stable is the neutron-to-proton ratio

as the mass number increases, the neutron-to-proton ratios become greater than one

for elements of low atomic number the value is close to one

nuclei that contain 2, 8, 20, 50, 82, and 126 protons are generally more stable (magic numbers)

nuclei with even numbers of both protons and neutrons are generally more stable than odd numbers

Nuclear Stability

If an isotope’s mass number is greater than its atomic weight, beta emission is expected

If an isotope’s mass number is less than its atomic weight, positron emission or electron capture is expected

All elements having an atomic number greater than 83 are radioactive. Alpha particles are emitted by most of these isotopes.

Nuclear Stability

a decay series

when a radioactive nucleus disintegrates, the products formed may also be unstable and under go further disintegration’s until a stable product is formed

U Pb238 20692 82

involves 14 steps

U238

92Pb

206

82

+U23892 Th

23490

42 He

+Th23490 Pa

23491

0-1 β

+Pa23491 U

23492

0-1 β

+U23492 Th

23090

42 He

+Th23090 Ra

22688

42 He

+Ra22688 Rn

22286

42 He

+Rn22286 Po

21884

42 He

+Rn22286 Po

21884

42 He

+Po21884 Pb

21482

42 He

+Pb21482 Bi

21483

0-1 β

+Bi21483 Po

21484

0-1 β

+Po21484 Pb

21082

42 He

+Pb21082 Bi

21083

0-1 β

+Bi21083 Po

21084

0-1 β

+Po21084 Pb

20682

42 He

all radioactive decays obey first-order kinetics

Kinetics of Radioactive Decay

Rate of decay at time t

= Nk

k = rate constant

the number of radioactive nuclei present at time t

N =

Time ( s )The plot shows the decay of uranium-238 to thorium-234

First-order rate plot

U23892 U Th +

238 23492 90

42 He

First-Order rate law Integrated

the integrated form of the rate law is:

t1/2 = k

0.693= kt

N0

Nt

ln

Integrated rate law

is an equation for a straight line

Plot ln Nt versus t

ln Nt = -kt + ln N0

y = mx + b

Slope = -k

y intercept is ln N0

Half-life

the time for the concentration of a reactant to decrease to one-half of its initial concentration

Time ( s )0

U23892

t 1/2 = 4.51 x 107yr

U Th +238 23492 90

42 He

Half-life

Radiocarbon Dating

Willard Libby (Nobel Prize, 1960)

Carbon-14

Natural abundance: 1 part in 1012

β − emitter

Half-life = 5730 yearsused to date archeological artifacts younger than 30,000 years

- +

14 C614 N7

0 e-1 +

Example

The C-14 decay rate of wood obtained from a live tree is 0.260 disintegration per second per gram of sample A sample of wood from an archaeological site has C-14 decay rate of 0.186 disintegration per second per gram. How old is the sample?

The C-14 decay rate of wood obtained from a live tree is 0.260 disintegration per second per gram of sample A sample of wood from an archaeological site has C-14 decay rate of 0.186 disintegration per second per gram. How old is the sample?

t 1/2 for 14C is known to be 5730 years

t1/2 = k

0.693

Therefore,k = (0.693/5730 yr)= 1.21 x 10-4 yr-1

ln[A]0

[A]= kt ln

260

186= (1.21 x 10-4 yr-1 ) t

t =2770 years

Some representative half-lives

Tc-99 6 hours

C-14 5730 years

Sr-90 28.8 years

Mo-99 67 hours

K-40 1,300,000 years

U-238 45, 000,000 years