the history of atomic theory the evolution of the atomic models early model bohr model- commonly...

The History of Atomic Theory

The Evolution of the Atomic Models

Early ModelBohr Model- commonly used model

Most Recent Model- Wave or Electron Cloud Model

The BeginningDemocritus- Atomos!

o Matter was: o indivisible.

o smallest piece of matter “atomos,” meaning “not to be cut.”

o small, hard particles

o Atoms were infinite in number, always moving and capable of joining together.

Other Theory of the time!!!• Devised by Aristotle and Plato

• Most popular and widely accepted theory.

• 4 basic types of matter in nature: – Earth – fire – air – water.

2000 Years Later…Dalton’s Theory (The 4 tenants)• All elements are composed of indivisible and indestructible atoms.

• Atoms of the same element are exactly alike and Atoms of different elements are different.

• Atoms combined in whole number ratios when forming compounds.

• Compounds are formed by a chemical reaction in which matter is not created nor destroyed.

Then…Thomson’s Model

• Atoms were a positively charged substance with negatively charged electrons scattered about, like raisins in a pudding.

Thomson Model• Studied using a Crookes tubes.• When electric current was passed through a

luminescent ray passed from one to another.– Thought these rays might be waves, atoms or

particles. • Thomson decided they had to be unique

particles within the atom. – Particles were 1000 times smaller then a H

atom. – Studied and found rays were same regardless

of material.

Thomson’s Conclusion: Ray was result of something with a negative charge coming from within atom.

A particle smaller than an atom had to exist.

Since the gas was neutral, having no charge, he reasoned that there must be positively charged particles in the atom.

But he could never find them.

Protons

• Eugene Goldstein- identified the proton using the same rays that Thomson discovered.

• Called these opposite rays- canal rays

Protons

• Protons are subatomic particles with a Protons are subatomic particles with a positive electric charge.positive electric charge.

• They are 2000 times larger than the They are 2000 times larger than the electron with a mass of 1.673×10−27 kg electron with a mass of 1.673×10−27 kg

• Not elementary particlesNot elementary particles–composed of the elementary particles, composed of the elementary particles,

quarks (2 ups and 1 down)quarks (2 ups and 1 down)• Quarks- elementary particles that make Quarks- elementary particles that make

up protons and neutrons.up protons and neutrons.

Rutherford’s contributions to the atom

• .Gold Foil Experiment• Fired a stream of tiny positively charged

particles at a thin sheet of gold foil (2000 atoms thick)

What did Rutherford conclude? – Most alpha particles

passed right through the gold foil-

• Conclusion: Atoms composed of empty space?

– Some Particles bounced away from the gold sheet as if they had hit something solid.

• Conclusion: Central positive charge repelling the positive charges.

Rutherford’s Theory

• Atoms are mostly open space.

• Atoms have a small, dense, positively charged center.

• Center was termed nucleus and determined to be tiny compared to the atom as a whole.

Neutrons• Neutrons-

– Made up of elementary particles

• 1 up and 2 downs

• James Chadwick- identified the neutron

– Studying alpha particles was able to knock heavy neutral particles out of the atom.

The nucleusNucleus is held together by 2 fundamental forces in nature:

– Strong force- force within protons or neutrons– Weak force- force between the particles of a

proton and neutron – Heavier atoms with more protons and neutrons

have a weaker force and therefore are more unstable and become radioactive. This is why elements towards the bottom of the periodic table are generally synthetic.

Measuring Atoms

• Remember the concept mole:

• 1 mole = 6.02 X 10 23 representative particles

• Suppose you wanted to measure how many particles are in 3 moles of Na.

• Using the relationship above you could convert from one unit into another.

• What would this look like?

Bohr and Wave models

Most recent discoveries and understandings:

Bohr Model: Most Common Model• Electrons move in

definite orbits around the nucleus.

• Orbits, or levels are located at certain distances from the nucleus.

Bohr Models

Electrons fill the energy levels like steps on a ladder.

Ring= energy levelOuter electrons: Valence

Electrons1st ring: 2 electrons2nd ring: 8 electrons 3rd ring: 18 electrons4th ring: 32 electrons5th ring: 50 electrons

Wave Model

The Wave Model• Today’s atomic

model is based on the principles of waves

• According to the wave theory, electrons do not move about an atom in a definite path, like the planets around the sun.

The Wave Model

• It is impossible to determine the exact location of an electron. – The probable location of an electron is based on how

much energy the electron has.

• Atoms have a small positively charged nucleus surrounded by a large region in which there are enough electrons to make an atom neutral.

Electron Cloud: the space of electrons

• A space in which electrons are likely to be found.

• Electrons whirl about the nucleus billions of times in one second

• They are not moving around in random patterns.

• Location of electrons depends upon how much energy the electron has.

Electron Cloud and The Wave Model

• Depending on their energy they are locked into a certain area in the cloud.

• Lowest energy electrons are found in the energy level closest to the nucleus

• Highest energy are found in the outermost energy levels, farther from the nucleus.

Electrons and Energy

• Electrons have specific amounts of energy based upon their location.

• Electrons can release energy giving off photons of light in process – Example: Bite into a Wintergreen lifesaver in

the dark. What do you notice? Why?

Farther Explained by Max Planck

Max Planck’s Quantum • Electrons travel in packets of energy-

quantum

These electrons release photons- light

This lead Einstein and Planck to believe that electrons travel as waves. Helps to explain the quantum mechanical model

ELECTRONELECTRON PROTONPROTON NEUTRONNEUTRON

SYMBOLSYMBOL ee-- pp++ nn00

RELATIVE RELATIVE CHARGECHARGE -1-1 +1+1 00

ACTUAL ACTUAL CHARGE CHARGE

(C)(C)

-1.602 x -1.602 x 1010−19−19

+1.602 x +1.602 x 1010−19−19 00

RELATIVE RELATIVE MASSMASS 00 11 11

ACTUAL ACTUAL MASS (kg)MASS (kg) 9.109 x 109.109 x 10-31-31 1.673 x 101.673 x 10-27-27 1.675 x 101.675 x 10-27-27

LOCATIONLOCATIONelectron electron

cloudcloud nucleusnucleus nucleusnucleus

The Atomic Structure

Atomic Structure

• Based on experimentation and research the following conclusions have been made: – Atoms are composed of protons, neutrons

and electrons.– Protons and neutrons are centralized in the

nucleus.– Electrons are found in the electron cloud in

specific energy levels that are not fixed.

Atomic Number vs. Mass Number

Protons- unique for each element Determine the Atomic Number Protons= atomic number

Neutrons- change mass of an element With protons determine the mass of an atom Protons + neutrons = mass number

Electrons- determine behavior of element Protons=electrons (atoms must be neutral)

CHEMICAL COMPOSITION SHORTHAND

CHEMICAL COMPOSITION SHORTHAND

ClCl3535

1717

MASS MASS NUMBERNUMBER

MASS MASS NUMBERNUMBER

ATOMIC ATOMIC NUMBERNUMBERATOMIC ATOMIC NUMBERNUMBER

NUMBER OF NUMBER OF PROTONSPROTONS

NUMBER OF NUMBER OF PROTONSPROTONS

# OF PROTONS# OF PROTONS++

# OF NEUTRONS# OF NEUTRONS

# OF PROTONS# OF PROTONS++

# OF NEUTRONS# OF NEUTRONS

Can Atoms of the same element differ?

• # of protons is unique to each element

• # of neutrons and electrons can change. – Isotopes- variation of neutrons

• Change of neutrons decreases or increases mass

– Ions- variation of electrons• Elements lose or gain electrons to become stable• “Octet rule” states elements need 8 valence

electrons in order to be stable “non reactive”

protonproton

neutronneutron

electronelectron

BERYLLIUMISOTOPES

BERYLLIUMISOTOPES

Isotopes

• Element with same amount of protons but different amounts of neutrons.

EXAMPLE OF AN ISOTOPE

EXAMPLE OF AN ISOTOPE

ClCl3535

1717 ClCl3737

1717

20 20 NEUTRONSNEUTRONS

ATOMIC MASSATOMIC MASS

1818 NEUTRONSNEUTRONS

ATOMIC NUMBERATOMIC NUMBERATOMIC NUMBERATOMIC NUMBER

Average Atomic Mass • Average mass of all

isotopes of an element• Relative to the other

elements around. • Determined by taking

the sum of mass of all the isotopes multiplied by their relative abundances

• Relative abundance: Percent abundance as a

decimal

Calculating Atomic mass

• Example: Rubidium has two common isotopes, 85Rb and 87Rb. If the abundance of 85Rb is 72.2% and the abundance of 87Rb is 27.8%, what is the average atomic mass of rubidium?

• (85 amu X .722) + (87 amu X .278) (61.37amu + 24.186 amu)

Answer: 85.56 amu

• Practice: Magnesium has three isotopes– Magnesium-24 78.70 % abundant– Magnesium-25 10.13% abundant– Magnesium-26 11.17% abundantDetermine average atomic mass of magnesium. Units are amus

Measuring atoms continued:

• What if instead you were given the number of particles.

• Calculate the number of moles that contain 4.50 x 1024 atoms of zinc (Zn).

The Quantum Mechanical Model

Where are electrons found in the atom?

• Heisenberg’s Uncertainty Principle-it is impossible to know the exact location and velocity of an electron at the same time.

• E= h Ʋ

E= energy,

h= plank’s constant

(6.63X 10-34 js)

Ʋ = frequency

How do electrons move to produce or give off energy?

• They can jump from energy level they are at up to the last energy level (n=7)

• As they jump to the different levels they give off different wavelengths of energy.– Lower energy- red, orange, yellow– Higher energy- green, blue, indigo, violet

Observing Electrons continued:Cannot see electrons,

but can see their energy

Travels as waves

Type of wave based on:

1)Amplitude

2)Wavelength

3)frequency

Electromagnetic Spectrum = Electron Waves

Atomic Spectrum

• Absorbed energy electrons move to higher energy levels

• Emit energy and return to lower energy levelsAppears as light (atomic emission spectrum)–Based on electron configuration (the fingerprints of an element)

Examples of Atomic Emission Spectrums

• As we observe the different gas tubes, notice how their bands.

• This is due to the fact that the element’s electron configuration changes, so its electrons can do different things.

• Example:

Organizing Electrons

Organization of these Electrons• Energy levels- determine the amount of energy an

electron has.

Energy levels= n = Principle quantum numbern= 1= 1st energy level n= 2 = 2nd energy level n=3= 3rd energy level

All the way up to the 7th energy level

Energy level → Sublevel →Orbital

Angular Quantum Number (sublevels)

•angular momentum quantum number (l) also known as the shape l= n-1 l= 0 (s sublevel)

l=1 (p sublevel)

l= 2 ( d sublevel)

l= 3 (f sublevel)

l= 4 (g sublevel)

l = 5 ( h sublevel)

Filling sublevels# of energy levels= #of sublevels

N=1 1 sublevel s

N=2 2 sublevels s and p

N= 3 = 3 sublevels = s, p and d

N = 4 = 4 sublevels = s, p, d and f

N=5 = 5 sublevels= s, p, d, f and g

N=6 = 6 sublevels = s, p, d, f, g and h

For the sake of this class we only see fill through the f sublevel

Orbitals (m1)

Orbitals= Areas of highest probability for electrons to be located... (magnetic quantum number-orientation of shape)

m1 = 2L + 1 = # of orbitals in sublevel

S= L = 0 so 1 orbital

P= L = 1 so 3 orbitals

D=L = 2 so 5 orbitals

F= L =3 so 7 orbitals

S Sublevel

P Sublevel

D sublevel

F sublevel

Electrons- Spin Quantum Number (m2)

• 2n2= # of electrons per energy level• Orientation of spin on the axis• Pauli exclusion principle-

– No two electrons in the same atom can have identical values for all four quantum numbers.

– Fill the orbitals with no more than 2 electrons in order to be stable and the 2 electrons in each orbital must have opposite spins.

• Spin in one of two directions (up or down)

• m2 = + ½ or – ½

Order of fill

Valence Electrons- Lewis Structures

Shows symbol of element surrounded by valence electrons.

Dots are used for each valence electron.

Can hold up to 8 electrons. Exception Helium that can hold 2.

Electron Dot Structure or Lewis Dot Diagram

A notation showing the valence electrons surrounding the atomic symbol.

How do lewis diagrams fill?

• Fill in the following order. Lets do some examples in class…

The Octet Rule- Ions

• “Goal” of most atoms (except H, Li and Be) is to have an octet or 8 valence electrons

• Accomplished by giving or taking electrons.

• Metals= give electrons

• Nonmetals= take electrons; except hydrogen

• Ions= atoms that have gained or lost electrons

Ions

• Anions: gaining electrons, becomes negatively charged (more electrons than protons)

• Cations: lose electrons; becomes positively charged (more protons than electrons)

SOME ATOMS GAIN ELECTRONS

SOME ATOMS GAIN ELECTRONS

O

--

----

--

--

--

--

--

O-2

--

----

--

--

--

--

--

----

ATOM’S IONIC CHARGE = ATOM’S IONIC CHARGE = # PROTONS - # ELECTRONS # PROTONS - # ELECTRONS

ATOM’S IONIC CHARGE = ATOM’S IONIC CHARGE = # PROTONS - # ELECTRONS # PROTONS - # ELECTRONS

Cation Formation

11p+

Na atom

1 valence electron

Valence e- lost in ion formation

Effective nuclear charge on remaining electrons increases.

Remaining e- are pulled in closer to the nucleus. Ionic size decreases.

Result: a smaller sodium cation, Na+

Anion Formation

17p+

Chlorine atom with 7 valence e-

One e- is added to the outer shell.

Effective nuclear charge is reduced and the e- cloud expands.

A chloride ion is produced. It is larger than the original atom.

Activity• Using bag of elements at your desk. Make

at least 5 electron dot diagrams and 5 ions for the elements in your bag. - 10 minutes

• Trade and grade

• Make 5 more electron dot diagrams and 5 more ions from different elements in your bag. – 10 more minutes.

Electron Configurations

How do the electrons organize?• Aufbau Principle

– Each electron occupies lowest energy orbital first

• Pauli Exclusion Principle– Orbitals hold up to 2 electrons and these

electrons must be spinning in opposite directions.

• Hund’s Rule– Electrons spinning in the same direction will fill a

sublevel before additional electrons with opposite spins will fill each orbital.

Electron Configurations

• Compilation of Bohr Model and Wave Model organize electrons into Energy levels.

• Electrons are organized so that one can see their exact location inside of an atom.

• Organization: – Energy level →Sublevel→ Orbital

Order

Parts of electron configuration

1s2# of electrons in sublevel

Sublevel

Energy level

↓

↑

←

Electron Configurations Examples:

• Hydrogen1s1

• Helium 1s2

• Lithium1s2 2s1

• Beryllium1s2 2s2

More Examples• Boron

1s2 2s2 2p1

• Carbon1s2 2s2 2p2

• Nitrogen1s2 2s2 2p3

• Oxygen1s2 2s2 2p4

• Fluorine1s2 2s2 2p5

• Neon1s2 2s2 2p6

In-class Practice

• Draw electron configurations for all elements in row 3.

Aufbau Principle

D an F orbitals

• First D orbital is in 3rd energy level.

• First F orbital is in the 4th energy level

Writing Configurations for D sublevel

• Scandium1s2 2s2 2p63s23p64s23d1

• Titanium1s2 2s2 2p63s23p64s23d2

• Vandium 1s2 2s2 2p63s23p64s23d3

The rest of this row would continue to add up until you get to d10. Then, you go back into p sublevel

Writing configurations for F sublevel

• Lanthanum1s2 2s2 2p63s23p64s23d104p65s24d105p66s24f1

Try Cerium1s2 2s2 2p63s23p64s23d104p65s24d105p66s24f2

Notice how you continue to add on to configuration until all electrons are used up…

• Write configurations for the following elements: – Mercury– Silver– Iodine– Uranium

Practice

Orbital Notation

• Each box represents an orbital in a specific energy level

• S sublevel = 1 box

• P sublevel = 3 boxes

• D sublevel= 5 boxes

• F sublevel = 7 boxes

Orbital Notation examples

Assignment

• Draw orbital diagrams for the following elements: – Row 2 and 3 elements– Silver– Iodine

Periodic Trends• Dmitri Mendeleev- discovered a trend

when elements were put in order of increasing atomic number they formed a regular and repeating pattern of chemical properties.

The Periodic Law

• Atoms with similar properties appear in groups or families (vertical columns) on the periodic table.

• They are similar because they all have the same number of valence (outer shell) electrons, which governs their chemical behavior.

Valence Electrons

• Do you remember how to tell the number of valence electrons for elements in the s- and p-blocks?

• How many valence electrons will the atoms in the d-block (transition metals) and the f-block (inner transition metals) have?

A Different Type of Grouping

• Besides the 4 blocks of the table, there is another way of classifying element:

• Metals

• Nonmetals

• Metalloids or Semi-metals.

• The following slide shows where each group is found.

Metals, Nonmetals, Metalloids

Metals, Nonmetals, Metalloids

• There is a zig-zag or staircase line that divides the table.

• Metals are on the left of the line, in blue.

• Nonmetals are on the right of the line, in orange.

Metals, Nonmetals, Metalloids

• Elements that border the stair case, shown in purple are the metalloids or semi-metals.

• There is one important exception.

• Aluminum is more metallic than not.

Metals, Nonmetals, Metalloids

• How can you identify a metal?

• What are its properties?

• What about the less common nonmetals?

• What are their properties?

• And what the heck is a metalloid?

Metals

• Metals are lustrous (shiny), malleable, ductile, and are good conductors of heat and electricity.

• They are mostly solids at room temp.

• What is one exception?

Nonmetals

• Nonmetals are the opposite.

• They are dull, brittle, nonconductors (insulators).

• Some are solid, but many are gases, and Bromine is a liquid.

Metalloids• Metalloids, aka semi-

metals are just that.• They have characteristics

of both metals and nonmetals.

• They are shiny but brittle.• And they are

semiconductors.• What is our most important

semiconductor?

Periodic Trends

• There are several important atomic characteristics that show predictable trends that you should know.

• The first and most important is atomic radius.

• Radius is the distance from the center of the nucleus to the “edge” of the electron cloud.

Atomic Radius

• Since a cloud’s edge is difficult to define, scientists use define covalent radius, or half the distance between the nuclei of 2 bonded atoms.

• Atomic radii are usually measured in picometers (pm) or angstroms (Å). An angstrom is 1 x 10-10 m.

Covalent Radius

• Two Br atoms bonded together are 2.86 angstroms apart. So, the radius of each atom is 1.43 Å.

2.86 Å1.43 Å 1.43 Å

Atomic Radius

• The trend for atomic radius in a vertical column is to go from smaller at the top to larger at the bottom of the family.

• Why?

• With each step down the family, we add an entirely new energy level to the electron cloud, making the atoms larger with each step.

Atomic Radius

• The trend across a horizontal period is less obvious.

• What happens to atomic structure as we step from left to right?

• Each step adds a proton and an electron (and 1 or 2 neutrons).

• Electrons are added to existing energy level and sublevels.

Atomic Radius

• The effect is that the more positive nucleus has a greater pull on the electron cloud.

• The nucleus is more positive and the electron cloud is more negative.

• The increased attraction pulls the cloud in, making atoms smaller as we move from left to right across a period.

Effective Nuclear Charge

• What keeps electrons from simply flying off into space?

• Effective nuclear charge is the pull that an electron “feels” from the nucleus.

• The closer an electron is to the nucleus, the more pull it feels.

• As effective nuclear charge increases, the electron cloud is pulled in tighter.

Atomic Radius

• The overall trend in atomic radius looks like this.

Atomic Radius

• Here is an animation to explain the trend.

• On your help sheet, draw arrows like this:

Shielding

• As more energy levels are added to atoms, the inner layers of electrons shield the outer electrons from the nucleus.

• The effective nuclear charge (enc) on those outer electrons is less, and so the outer electrons are less tightly held.

Ionization Energy• This is the second important periodic

trend.• If an electron is given enough energy (in

the form of a photon) to overcome the effective nuclear charge holding the electron in the cloud, it can leave the atom completely.

• The atom has been “ionized” or charged.• The number of protons and electrons is no

longer equal.

Ionization Energy

• The energy required to remove an electron from an atom is ionization energy. (measured in kilojoules, kJ)

• The larger the atom is, the easier its electrons are to remove.

• Ionization energy and atomic radius are inversely proportional.

• Ionization energy is always endothermic, that is energy is added to the atom to remove the electron.

Ionization Energy

Ionization Energy (Potential)

• Draw arrows on your help sheet like this:

Electron Affinity

• What does the word ‘affinity’ mean?

• Electron affinity is the energy change that occurs when an atom gains an electron (also measured in kJ).

• Where ionization energy is always endothermic, electron affinity is usually exothermic, but not always.

Electron Affinity

• Electron affinity is exothermic if there is an empty or partially empty orbital for an electron to occupy.

• If there are no empty spaces, a new orbital must be created, making the process endothermic.

• This is true for the alkaline earth metals and the noble gases.

Electron Affinity

• Your help sheet should look like this:

++

Metallic Character

• This is simple a relative measure of how easily atoms lose or give up electrons.

• Your help sheet should look like this:

Electronegativity• Electronegativity is a measure of an atom’s

attraction for another atom’s electrons.

• It is an arbitrary scale that ranges from 0 to 4.

• The units of electronegativity are Paulings.

• Generally, metals are electron givers and have low electronegativities.

• Nonmetals are electron takers and have high electronegativities.

• What about the noble gases?

Electronegativity

• Your help sheet should look like this:

0

Overall Reactivity• This ties all the previous trends together

in one package.

• However, we must treat metals and nonmetals separately.

• The most reactive metals are the largest since they are the best electron givers.

• The most reactive nonmetals are the smallest ones, the best electron takers.

Overall Reactivity

• Your help sheet will look like this:

0

All trends

Nuclear reactions

The four forces of Nature

• Strong force- the force holding neutrons and protons together

• Weak force- the force holding neutrons together• Electromagnetic force- the force that attracts

positive and negative charges.• Gravity- the force that pulls matter towards each

other

• In order of decreasing energy (Strongest energy is the force holding the nucleus together)

What is nuclear decay?• Unstable nuclei naturally

break down.

• The greater the difference between neutrons and protons the more likely the break down.

• As this break down occurs radioactivity is given off.

What is given off by radioactive decay?

• Alpha particles

• Beta particles

• Gamma particles

Where do these particles come from ?

•From the nuclei of unstable atomic isotopes.

• Uranium decay produces all three of these forms of radiation.

• Let’s look at them in more detail…

Alpha Particles ()

Radium

R226

88 protons138 neutrons

Radon

Rn222

Note: This is theatomic weight, whichis the number ofprotons plus neutrons

86 protons136 neutrons

+ nnp

p

He)

2 protons2 neutrons

The alpha-particle is a Helium nucleus.

It’s the same as the element Helium, with no electrons!

Beta Particles ()

CarbonC14

6 protons8 neutrons

NitrogenN14

7 protons7 neutrons

+ e-

electron(beta-particle)

A neutron from the C14 nucleus is “converted” into a proton, and an electron was ejected.

The remaining nucleus contains 7p and 7n, which is a nitrogen nucleus. In symbolic notation, the following process occurred:

Gamma particles ()In much the same way that electrons in atoms can be in an excited state, so can a nucleus.

NeonNe20

10 protons10 neutrons

(in excited state)

10 protons10 neutrons

(lowest energy state)

+

gamma

NeonNe20

A gamma is a high energy light particle.

It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.

A gamma is a high energy light particle.

It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.

Gamma Rays

NeonNe20 +

The gamma from nuclear decayis in the X-ray/ Gamma ray

part of the EM spectrum(very energetic!)

NeonNe20

How do these particles differ ?

ParticleMass*

(MeV/c2)Charge

Gamma () 0 0

Beta () ~0.5 -1

Alpha () ~3752 +2

* m = E / c2* m = E / c2

What do these particles pentrate?

Nuclear Decay Series

Uranium has an atomic number greater than83. Therefore it is naturally radioactive.

Most abundant isotope

Alpha Particle

Thorium Decay

Of course Thorium’s atomic number is alsogreater than 83. So it to is Radioactive andGoes through beta decay.

234Pa + 0e91 -1

Protactinium

Predicting the Product of a Nuclear Reaction- AlphaWhat product is formed when radium-226 undergoes alpha decay?

What product is formed when polonium-212 undergoes alpha decay?

Predicting products of nuclear decay- beta

• Remembering thorium from the previous slide, predict what will happen to Potassium-40 if it undergoes beta decay.

Rate of Decay• How frequently atoms emit radiaton or how long does it take for atoms to decay?• Cannot predict when a particular entity will decay.

•But can predict when a number in a large sample will decay. Called a radioactive half-life

• Decay rate- •some atoms break down extremely quickly- Uranium-231•Some atoms break down slowly- Carbon-14

Half-Life• “Half-life” (h) = time it takes for half the atoms of a radioactive substance to decay.•Example:

•we had 20,000 atoms of a radioactive substance. If the half-life is 1 hour, how many atoms of that substance would be left after:

10,000 50% or 1/2

5,000 25% or 1/4

2,500 12.5% or 1/8

1 hour

2 hours

3 hours

Time #atoms

remaining% of atomsremaining

Half-life equation• Nt = No X (.5)n

Nt = amount of sample remaining

No = initial amount of sample

n= # of half-lifes

Or

• Mt = Mo X (.5)n

Mt = mass of sample remaining Mo = mass of initial sample

Problem:A sample of Iodine-131 had an original

mass of 16g. How much will remain in 24

days if the half life is 8 days?

Problem:• What is the ½ life of a sample if after 40

years 25 grams of an original 400 gram sample is left ?

142

Problem:• You have 400 mg of a radioisotope with a

half-life of 5 minutes. How much will be left after 30 minutes?

143

problem:• Cobalt-60 is a radioactive isotope used

in cancer treatment. Co-60 has a half-life of 5 years. If a hospital starts with a 1000 mg supply, how many mg will need to be purchased after 10 years to replenish the original supply?

Homework:

• Find an article on the use of radioactive decay in medicine. Research this and determine the risks and benefits of this material and it’s use. Bring in your thoughts for discussion.