Do Now (3/17/14):

1.What are some words and images that come to mind when you hear the word “radioactivity”?

2.What is an isotope?

3.What makes an isotope different than its element?

Radioactivity 4/23/12

Lesson Objectives

Describe nuclear reactions and perform balancing of nuclear reactions by solving problems.

Apply radioactivity equations by solving problems.

Nuclear reaction

A reaction in which the number of protons or neutrons in the nucleus of an atom changes.

Atomic number

Number of protons in the nucleus of the atom

Mass number

Sum of protons and neutrons in the nucleus of the atom

Alpha decay

Radioactive decay process in which the nucleus of an atom emits an alpha particle

Alpha Particle

Nucleus of a helium atom

Beta decay

Radioactive decay that occurs when a neutron is changed to a proton within the nucleus of an atom, and a beta particle and an antineutrino are emitted

Gamma decay

Radioactive process of decay that takes place when the nucleus of an atom emits a gamma ray.

http://library.thinkquest.org/17940/texts/radioactivity/radioactivity.html

Isotope

Atomic nuclei having the same number of protons but different number of neutrons

All Elements Have Radioactive Isotopes

All elements have more than one isotope Some isotopes of all elements are

radioactive Some half-lives are so short that the isotope

is not found naturally Radioactive Isotope display

A Half-Life Is the Time Required for ½ the Atoms of a Substance to Undergo Radioactive

Decay Applet Animation

T1/2 = time for half the sample             to disintegrate----------------------------------------Assume T1/2   =  5 years ----------------------------------------Number of nuclei present attime t = 0:

N0     = 1000---------------------------------------When t = 5 yrs,    N = 50 t = 10 yrs,   N = 250 t = 20 yrs,   N = 125.

Calculate the half-life animation

Applet Animation

Half Life:

Half-life: time needed for half of remaining mass of element to decay

t (# halflives)T12

Example #1:

Fermium-253 has a half-life of 0.334 seconds. A radioactive sample is considered to be completely decayed after 10 half-lives. How much time will elapse for this sample to be considered gone?

Decay Rate

T1/2=half life

λ=decay rate

0.693

T12

Example #2:

The half life of Zn-71 is 2.4 minute. If one had 100 g at the beginning, what is the decay rate of Zn-71?

Mass remaining

m=mass remaining

Original mass

m m0e t

Example #3:

The half life of Zn-71 is 2.4 minute. If one had 100 g at the beginning, how many grams would be left after 7.2 minutes elapsed?

Practice:

Use the rest of class to work on the paper: Radioactivity; problems: #2,5,6, and 7

Do Now (4/24/12):

Pd-100 has a half-life of 3.6 days. If one had 6.02x1023 atoms at the start, how many atoms would be present

Do Now (4/24/12):

U-238 has a half-life of 4.46x109 years. How much U-238 should be present in a sample 2.5 x10 10 years old, if 2 grams were present initially?

Using Logarithms

m m0e t

m

m0e t

Using Logarithms

m

m0e t

lnm

m0

t

Using Logarithms

Solving for λ:

lnm

m0

t

Using Logarithms

Solving for t:

t lnm

m0

The Uranium Decay Series

The only radium that exists today is that which is created as a result of the decay of uranium.

Decay series animation

Carbon-14 Production

Neutron enters nucleus and kicks out a proton.                    0n

1  +  7N14 --------->  6C

14  + 1p1

Carbon-14 Enters the Ecosystem

Carbon Dating

Since living organisms continually exchange carbon with the atmosphere in the form of carbon dioxide, the ratio of C-14 to C-12 approaches that of the atmosphere.

From the known half-life of carbon-14 and the number of carbon atoms in a gram of carbon, you can calculate the number of radioactive decays to be about 15 decays per minute per gram of carbon in a living organism.

Measuring the Age of Organic Matter

A German tourist in theItalian Alps discoveredthe remains of the "Iceman" in the ice of aglacier in 1991.  

Calculating the Iceman's Age

The current activity per gram ofcarbon half what it would be ifthe Iceman were alive.

Since the half-life of carbon-14is about 5700 years, theIceman's remains are about5700 years old.

Radioactivity Equations

N(t)  =  population at time t

N(0) =  population at time zero

N0   =   N(0)

l     =   decay constant

  N(t) = N0 e-lt  

Example:    N0 = 1000

l = 2 x 10-3 years -1

When will N = 200? N   = N0 e

-lt                  

  (1) e-lt = N /N0                  

   (2) ln (e-lt) = ln (N /N0)        

(3) -l t = ln (N /N0)           

 (4) t = - [ln (N /N0)] / l              (5)

= - [ln (200/1000)] /2 x10-3      (6) =  805 years

Half-Life Problem

The half-life of a radioactive substance is10 hours.   What is the decay constant, l?--------------------------------------------------------N = N0 e

-lt                                    (1)

0.50 N0 = N0 e-l10                       (2)

e-l10 = 0.50                                  (3)

ln(e-l10) = ln(0.50)                       (4) -10 l  = -0.693                        (5) l   = 0.0693 hrs-1              (6) 

Half-Life Problem

From the previous problem, how much time will it take for the sample's activity to fall to only 20% of what it was originally?----------------------------------------------N = 0.20 N0                              (7)

0.20 N0 = N0 e-0.0693 t             (8)

-0.0693 t = ln (0.20)                  (9)

t = 23 hours

Decay Constant and Half-Life

N = N0 e-lt                    (1)

0.50 N0 =  N0 e-lT                  (2)

(T = half-life)       e-lT =  0.50                       (3)

 ln(e-lT) =  ln(0.50)                   (4) -lT =  -0.693                    (5)  T =  0.693/l                   (6)

l  = 0.693/T                   (7)

Half-Life Example

38Sr90 (strontium-90) has a half-life of 28.5 years.

How long will it take for 98% of a sample of strontium-90 to disappear?------------------------------------------------------------------l  = 0.693/T1/2

= 0.693 / 28.5 = 0.0243 years-1

   

0.02 = e-0.0243 t t = - ln(0.02) /0.0243 years-1

=  161 years

Radioactivity Units

A  =  number of disintegrations

         per second, activity

A  = lN      

One becquerel (Bq) is one disintegration per second.  

One curie is the number of disintegrations per second (the "activity") of one gram of radium, or about 3.7 x 10 10 Bq.

Units of Absorbed Radiation

Rad:    10 milli-joules per kilogram 

20 rads of X-rays doesn't do the same damage to humans as 20rads of alpha particles.----------------------------------------------Rem:  an absolute biological           damage unit

Radiation Sickness

Dose(rems)          Effect

50-300 Sickness

400-500 Lethal   50%   (LD50)

Above 600 Lethal 100%   (LD100)

Calculate Rems from Rads (Relative Biological

Effectiveness)

Radiation R(rems/rad)

a-particles  20

Neutrons  10

Protons  10

b-particles    1

g-rays    1

X-rays    1

Example:

How many rads of protons will kill a person?------------------------------600 rems is fatal RBE for protons is 10

Number of rads = 600 / 10                         = 60

Example:

One joule of energy per kilogram is absorbed in the form of neutrons.

Will this prove fatal?--------------------------------1 rad is ten milli-joules

1 rad = 0.010 J

Radon Poisoning

Uranium in earth's crust decays to radium, which decays to radon.

Radon is an odorless, tasteless, lighter-than-air gas which rises from the ground through cracks and fissures in the earth into homes. When breathed, the alpha-emitting radon can cause cancer of the lung.

Radon is the single greatest source of radiations for humans, providing about 200 milli-rems per year per person.

Practice:

Complete any four problems from the Radioactivity Worksheet

When you are finished, raise your hand so I can stamp it

Bring this paper to school with you this week!