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Modern Physics

Thanks to:Dr. P. BertrandOak Ridge HS

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Quantum Physics Physics on a very small (atomic) scale is

“quantized”. Quantized phenomena are discontinuous and

discrete, and generally very small. Quantized energy can be throught of an

existing in packets of energy of specific size. Atoms can absorb and emit quanta of energy,

but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.

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Electromagnetic Spectrum

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Light is a ray

We know from geometric optics that light behaves as a ray; it travels in a straight line.

When we study ray optics, we ignore the nature light, and focus on how it behaves when it hits a boundary and reflects or refracts at that boundary.

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But light is also a wave!

We studied this earlier in the year and we will use this equation again here.

C = f C: 3 x 108 m/s (speed of light in a

vacuum) f: frequency (Hz or s-1) : wavelength (m) (distance from crest

to crest)

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In quantum physics, we focus on how light behaves as a particle!

Light has a dual nature. In addition to behaving as a wave, it also behaves as a particle.

It has energy and momentum, just like particles do. Particle behavior is pronounced on a very small level, or at very high light energies.

A particle of light is called a “photon”.

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Calculating photon energy The energy of a photon is calculated

from the frequency of the light. E = hf = hc / because c = f E = nhf (for multiple n # of photons)

E: energy (J or eV) h: Planck’s constant

6.625 x 10-34 J s (SI system) 4.14 x 10-15 eV s (convenient)

f: frequency of light (s-1, Hz)

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Checkpoint Which has more energy in its photons,

a very bright, powerful red laser or a small key-ring red laser? Neither! They both have the same energy

per photon; the big one has more power. Which has more energy in its photons,

a red laser of a green laser? The green one has shorter wavelength

and higher frequency. It has more energy per photon.

Quantum Double-Slit Experiment

https://www.youtube.com/watch?v=fwXQjRBLwsQ

Dr. Quantum https://www.youtube.com/watch?v

=h0hwuyOmd4k Einstein – History Channel

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The “electron volt” (eV)

The electron volt is the most useful unit on the atomic level.

If a moving electron is stopped by 1 V of electric potential, we say it has 1 electron volt (or 1 eV) of kinetic energy.

1 eV = 1.602 x 10-19 J

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Sample Problem

What is the frequency and wavelength of a photon whose energy is

4.0 x 10-19 J?E = hff = E/h =c = f = c/f =

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Sample Problem The bonding energy of H2 is 104.2 kcal/mol.

Determine the frequency and wavelength of a photon that could split one atom of H2 into two separate atoms. (1 kcal = 4l86 J).

E = (104.2 kcal)(4186 J)( 1 mol ) mol kcal 6.02x10 23mol’cls E = 7.24 x 10-19 J = hf f = 7.24 x 10-19 J/ 6.625 x 10-34Js f = 1.09 x 1015 Hz ***

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Atomic Transitions How many photons are emitted per second

by a He-Ne laser that emits 3.0 mW of power at a wavelength of 632.8 nm?

P = Etot /t E = hf P = n(hf)/t

c = f f = c/ P = nh(c/ ) n = (P)(t)() t (c)(h)

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SolutionFind total energy in one second from powerP = W/t = E tot / t

E tot = Pt = 3.0 x 10 -3 JNow see how many photons, n, will produce this

energyE = hf (one photon)E tot = nhf (for n photons)E = nhc/ (since wavelength is given and not

frequency)3.0x10-3 = n (6.625x10-34Js)(3.0x108m/s)/632.8x10-9mn = 9.55 x 1016

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General Info re the Atom

Atoms are composed of Nuclei (protons and neutrons) and

electrons When an atom encounters a photon

It usually ignores the photon, but sometimes absorbs the photon

If an atom absorbs a photon The photon disappears and gives all its

energy to the atom’s electrons

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Quantized atomic energy levels

*This graph shows

allowed quantized

energy levels in a

hypothetical atom.

*The more stable states

are those in which the

atom has lower energy.

*The more negative the

state, the more stable

the atom.

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Quantized atomic energy levels The highest allowedenergy is 0.0 eV. Abovethis level, the atom losesits electron, This level iscalled the ionization or dissociation level. The lowest allowed energyis called the ground state.This is where the atom ismost stable. States between the highestand lowest state are calledexcited states.

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Transitions of theelectron within theatom must occur fromone allowed energylevel to another. The atom CANNOTEXIST betweenenergy levels.

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Absorption of photon by atom When a photon of light is absorbed

by an atom, it causes an increase in the energy of the atom.

The photon disappears. The energy of the atom increases

by exactly the amount of energy contained in the photon.

The photon can be absorbed ONLY if it can produce an “allowed” energy increase in the atom.

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Absorption of photon by atom

When a photon isabsorbed, itexcites the atomto higher quantumenergy state. The increase inenergy of the atom is given by E = hf.

Ground state

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Absorption Spectrum

• When an atom absorbs photons, it removes the photons from the white light striking the atom, resulting in dark bands in the spectrum.

• Therefore, a spectrum with dark bands in it is called an absorption spectrum.

Absorption spectrum seen through hand held spectroscope

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Absorption Spectrum

Absorptionspectraalways involveatoms going up in energylevel.

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Emission of photon by atom When a photon of light is emitted

by an atom, it causes a decrease in the energy of the atom.

A photon of light is created. The energy of the atom decreases

by exactly the amount of energy contained in the photon that is emitted.

The photon can be emitted ONLY if it can produce an “allowed” energy decrease in an excited atom.

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Emission of photon by atom

• When a photonIs emitted fromAn atom, theAtom drops toA LowerQuantumEnergy state.• The drop in energy can be computed by E = -hf.

E = -hf

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Emission Spectrum

• When an atom emits photons, it glows! The photons cause bright lines of light in a spectrum.

• Therefore, a spectrum with bright bands in it is called an emission spectrum.

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Emission of photon by atom

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Sample Problem

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Solution

***

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Photoelectric Effect #1• Sample Problem

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Solution

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Sample Problem

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Solution

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Atoms absorbing photons increase in energy

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Question

Now, suppose a photon with TOO MUCH ENERGY encounters an atom?

If the atom is “photo-active”, a very interesting and useful phenomenon can occur…

This phenomenon is called thePhotoelectric Effect.

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Photoelectric EffectE = work function + K

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Photoelectric Effect

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Sample Problem

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Solution

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Photoelectric Effect #2

• Sample Problem

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Sample Problem

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Solution

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Review of Photoelectric Effect

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Question

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The Photoelectric Effect Experiment

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Photoelectric Effect

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Strange results in the Photoelectric Effect experiment

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Voltage versus current for differentintensities of light

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Voltage versus current fordifferent frequencies of light

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Experimental determination of theKinetic Energy of a photoelectron

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Graph of Photoelectric Equation

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Photoelectric simulations

• http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm

• This is a link for a simulated photoelectric effect experiment

• Another link:

http://zebu.uoregon.edu/%7Esoper/Light/atomspectra.html

• ***

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Mass of a Photon

• Photon do not have “rest mass”. They must travel at speed of light and nothing can travel at the speed of light unless it has mass = zero.

• A photon has a fixed amount of energy (E = hf)

• We can calulate how much mass would have to be destroyed to create a photon (E=mc2)

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Sample Problem

• Calculate the mass that must be destroyed to create a photon of 340 nm light.

Emass = Ephoton

mc2 = hf = hc / m = h = h c cm = (6.625 x 10-34 kgm2/s2 x s) = (3x 10 8 m/s)(340 x 10 -4 m)

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Momentum of Photonp = mv = mc(c/c)=mc2/c = E/c = hf/c = h/

• Photon do not have “rest mass”, yet they have momentum! This momentum is evident in that, given a large number of photons, they create a pressure?

• A photon’s momentum is calculated by

p = E = hf = h

c c

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Experimental proof of the momentum of photons

• Compton scattering– High-energy photons collided with electrons

exhibit conservation of momentum– Work Compton problems just like other

conservation of momentum problems - except the momentum of a photon uses a different equation.

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Sample Problem

• What is the momentum of photons that have a wavelength of 620 nm?

p = h = 6.625 x 10 -34 kgm2/s2 x s

620 x 10 -9 m

= __________________kgm/s

kgm/s mass x velocity

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Sample Problem

• What is the frequency of a photon that has the same momentum as an electron with speed of 1200 m/s?

p e = p p

meve = h/ = h/c/f = hf/c

f = mevec/h

f = (9.11x10 -31 kg)(1200m/s)(3x108m/s)

6.625 x 10 -34 kgm2/s2 x s

f = ________________s-1

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Wave-Particle Duality

• Waves act like particles sometimes and particles act like waves sometimes.

• This is most easily observed for very energetic photons (gamma or x-Ray) or very tiny particles (electrons or nucleons)

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Particles and Photons both have Energy

• A moving particle has kinetic energy.– E = K = ½ mv2

• A particle has most of its energy locked up in its mass.– E = mc2

• A photon’s energy is calculated using its frequency.– E = hf

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Particles and Photons bothhave Momentum

• For a particle that is moving– p = mv

• For a photon– p = h/– Check out the units! They are those for

momentum.

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Particles and Photons bothhave Wavelength

• For a photon– = c/f

• For a particle, which has an actual mass, this equation still works– = h/p where p = mv– This is referred to as the deBroglie

wavelength

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Experimental proof that particles have wavelength

• Davisson-Germer Experiment– Verified that electrons have wave properties

by proving that they diffract– Electrons were “shone” on a nickel surface

and acted like light by diffraction and interference

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Problem

• What is the momentum of photons that have a wavelength of 620 nm?

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Sample problem

What is the wavelength of a 2,200 kg elephant running at 1.2 m/s?

p = h/ = h/p = h/mv

= 6.625 x 10-34 Js

(2200kg)(1.2m/s)

elephant = 2.51 x 10-37 m

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Naming a Nucleus

• Physicists Chemists

• Mass # Electronic Chg on

• atom or molecule

• Charge # # atoms in molec.

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Most common isotope of carbon

12

6C

Mass Number: protons plus neutrons

Atomic number: protons

Element symbol

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Isotopes

• Isotopes have the same atomic number but different atomic mass.

• Isotopes have similar or identical chemistry.

• Isotopes have different nuclear behavior.

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Uranium Isotopes

238 235

U U 92 92

Low Radioactive Fission

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Nuclear Particles

Proton Mass: 1 amu

Charge: +e

NeutronMass: 1 amu

Charge: 0

(1 amu = 1/12 mass of Carbon 12 atom)

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Electrons

Negative 0

e -1

Positive 0

e +1

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Nuclear Reactions

• Nuclear Decay - a spontaneous process in which an unstable nucleus ejects a particle and changes to another nucleus.– Alpha decay– Beta decay

• Beta Minus• Positron

• Fission - a nucleus splits into two fragments of roughly equal size

• Fusion - Two nuclei combine to form a heavier nucleus.

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Decay Reactions• Alpha decay

– A nucleus ejects an alpha particle, which is just a helium nucleus

• Beta decay– A nucleus ejects a negative electron

• Positron decay– A nucleus ejects a positive election

• Simulations: Nuclear Reactions– https://www.youtube.com/watch?v=50RWvXmQcFk (Bozeman)

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Nuclear Decay

Radiation and radioactive decay (Bozeman): https://www.youtube.com/watch?v=oFdR_yMKOCw

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Alpha Decay

• This occurs when a helium nucleus is released.

• This occurs only with very heavy elements.

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Beta (-) Decay

• A beta particle (negative electron) is released when a nucleus has too many neutrons for the protons present. A neutron converts to a proton and electron leaving a greater number of protons. An antineutrino is also released.

+

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Positron (+) Decay

• Positron decay occurs when a nucleus has too many protons for the neutrons present. A proton converts to a neutron. A neutrino is also released.

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Neutrino and Anti-Neutrino …

• Proposed to make beta and positron decay obey conservation of energy.

• Possess energy and spin, but do not possess mass or charge.

• Do not react easily with matter and are extremely hard to detect.

Neutrino & Antineutrino Production

Neutrinos are produced in nuclear reactions in the Sun when:

4protons --> alpha particle + 2p+ + 2neutrinos

Antineutrinos are produced by natural radioactivity in the Earth by the decay of 238U and 232Th

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Gamma Radiation, h

This isotope of radium has a small percentage of

particles that don't have their full energy; instead the nucleus is left excited and emits gamma rays.

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Complete the reaction and identify the type of decay:

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Complete the reaction for the alpha decay of Thorium-232.

+

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Fission and Fusion

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Fission Occurs when an unstable, heavy nucleus split

apart into two lighter nuclei (new elements). Can be induced by free neutrons. Mass is destroyed and energy produced

according to E = mc2. http://library.thinkquest.org/17940/texts/

fission/fission.html http://www.atomicarchive.com/Movies/

index.shtml www.atomicarchive.com/Movies/Movie4.shtml

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Neutron-induced fission

Produces a chain reaction Nuclear power plants operate by

harnessing the energy released in fission by controlling the chain reaction of U-235.

Nuclear weapons depend upon the initiation of an uncontrolled fission reaction

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U-235 bombarded with a neutron eads to an exponential growth of chain reactions.

A single U-235 fuel pellet the size of a fingertip contains as much energy as 17,000 cubic feet of natural gas, 1,780 pounds of coal or 149 gallons of oil.

For more information: http://www.nei.org/howitworks/nuclearpowerplantfuel/

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Naturally occurring uranium consists of three isotopes: uranium-234, uranium-235 and uranium-238. Although all three isotopes are radioactive, only uranium-235 is a fissionable material that can be used for nuclear power.

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Uranium-238, uranium's most common isotope, can be converted into plutonium- 239, a fissionable material that can also be used as a fuel in nuclear reactors. To produce plutonium-239, atoms of uranium-238 are exposed to neutrons. Uranium-239 forms when uranium-238 absorbs a neutron. Uranium-239 has a half-life of about 23 minutes and decays into neptunium-239 through beta decay. Neptunium-239 has a half-life of about 2.4 days and decays into plutonium-239, also through beta decay.

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Critical Mass

The neutrons released from an atom that has undergone fission cannot immediately be absorbed by other nearby fissionable nuclei until they slow down to “thermal” levels.

A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction.

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Nuclear Reactors

Nuclear reactors produce electrical energy through fission.

Advantages: a large amount of energy is produced without burning fossil fuels or creating greenhouse gases.

Disadvantage: produces highly radioactive waste.

Simulation: http://video.google.com/videosearch?q=nuclear+power+plant+operation&hl=en&emb=1&aq=f#

http://www.howstuffworks.com/nuclear-power.htm

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Fission

Occurs only with very heavy elements since fissionable nuclei are too large to be stable.

A charge/mass calculation is performed to balance the nuclear equation.

Mass is destroyed and energy is produced according to E = mc2.

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Problem: complete the following reaction and determine the energy released.

?

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Fusion Occurs when 2 light nuclei come together to

form a new nucleus of a new element. The most energetic of all nuclear reactions. Produced on the sun. Fusion of light elements can result in non-

radioactive waste. Proton-Proton Reaction

www.chemistrydaily.com/chemistry/Nuclear_reaction

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Fusion The reaction that powers the sun.

It has not been reliably sustained on earth in a controlled reaction.

Advantages: tremendous energy produced and lack of radioactive waste products.

Disadvantages: too much energy to control.

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Mass defect… How much mass is destroyed when a

nucleus is created from its component parts.

Generally much less than the mass of a proton or neutron, but it is still significant.

This loss of energy results in the creation of energy according to E = mc2.

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Calculating energy released innuclear reactions

1. Add up the mass (in atomic mass units, u_ of the reactants. Use your book.

2. Add up the mass ( in amu’s) of the products.

3. Find the difference between reactant and product mass. The missing mass has been converted into energy.

4. Convert mass to kg (1 u = 1.66x10-27 kg)5. Use E = mc2 to calculate energy released.

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What is the mass defect of 12C in atomic mass units? How does this relate to mass in kg and energy in eV and J?

6 1n + 6 1H 12C 1amu=1.66x10-27 kg 0 1 E =eV, e =1.6x10-19CMass of reactants (6 neutrons, 6 protons)6(1.008665 amu)+6(1.0078225 amu)

=12.09894Mass of product : 1(12.000) =12.00000 m = 0.09894 E=1.476x10-11J=92MeV 1.6x10-19J/eV

m=(0.09894u)(1.66x10-27kg/u)

m=1.4x10-28kg

E = mc2 = (1.4x10-28kg)(3x108m/s)2

E = 1.476 x 10-11J

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Problem

When a free proton is fused with a free neutron to form a deuterium nucleus, how much energy is released?

Mass of 1 proton = 1.0078225 amu Mass of 1 neutron = 1.008665 amu

Mass on the left:1.008665 +1.0078225 =

2.0164875uOn the right: 2.000Mass defect: 0.0164875

u

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Radioactive Decay of Bismuth-

210 (T½ = 5 days)

Translation: “The half life of Bismuth-210 is 5 days.”

Radioactive Decay of Bismuth-210 (T½ = 5 days)

The half life for bismuth is 5 days.

At the end of 5 days there is 50 g remaining

After 10 days 25 g

After 15 days 12.5 g

What is happening to the radioactive bismuth?

Half Life Problem

Tritium (H-3) has a half life of 12.3 yr. How much of a 1.0 g sample will remain after 24.6 yr?

24.6yr 1 h.l. = 2 h.l. 12.3 yrSample = 1.0 g = 0.25 g remaining2 xh.l. 2 2h.l.

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