nuclear reactions (chap. 31.1-31.4, Chap.32.3)

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(3) Determine mass number and charge of a nucleus after it has undergone specified decay ..... What would the kinetic energy of the electron be for problem #2?

AP B Physics: Unit XIII Modern Physics….

Part C: nuclear reactions (chap. 31.1-31.4, Chap.32.3)

Objectives- Nuclear (no half-life problems) 1. Nuclear reactions (including conservation of mass number and charge) � (1) Interpret symbols for nuclei that indicate these quantities. � (2) Use conservation of mass number and charge to complete nuclear reactions. � (3) Determine mass number and charge of a nucleus after it has undergone specified decay processes. � (4) Students should know the nature of the nuclear force, so they can compare its strength and range with those of the electromagnetic force. � (5) Students should understand nuclear fission, so they can describe a typical neutron-induced fission and explain why a chain reaction is possible.

2. Mass-energy equivalence Students should understand the relationship between mass and energy (mass-energy equivalence), so they can: � a) Qualitatively relate the energy released in nuclear processes to the change in mass. � 2

b) Apply the relationship E=mc in analyzing nuclear processes.


Misconceptions 1. Only fission reactions can give off energy, not fusion 2. All nuclear reactions result in creating a new element 3. Isotopes are actually different elements, not the same element with more neutrons 4. Neutrons and protons have the exact same mass 5. A neutron cannot decay into a proton 6. Stars give off energy due to fission 7. Mass is not energy 8. The nucleus of an atom weights more than the sum of its protons and neutrons 9. The ground is warm due to the Sun, not the radioactivity inside of the Earth. 10. All radiation is ionizing, that is, it will excite an electron to a higher level. 11. Over very short (sub-atomic) distances, electrostatic is stronger than the nuclear force. 12. During nuclear reactions, mass-energy is not conserved. 13. During nuclear reactions, the number of protons or neutrons is not conserved 14. Unlike a nuclear bomb, a nuclear reactor is based on a chained reaction 15. A nuclear reactor works better using faster not slower neutrons to start the reaction

Just for laughs… 

A neutron walks into a bar and orders a drink, so the barman puts one up on the counter. "How much?" asks the neutron. "For you", says the barman, "no charge.". The neutron says, “are you sure?” The barman says “I’m positive”! The neutron thinks what a quark! I beta decay not ever become a proton.oops, too late!


Constants atomic unit “u”= 1.66x10-27kg = 931.5 MeV speed of light “c” = 3.0 x 108m/s neutron mass=1.675 x10-27kg= 1.0087u proton mass= 1 .673 x10-27kg= 1.0073u electron mass= 9.11 x10-31kg=.0005u electron volt: eV= 1.6 x 10-19 J Equations: Energy due to mass or change in mass: E= m*c2 ( binding energy of a fused nucleus or kinetic energy of fission products)  Symbols to recognize:  = 42 He alpha particle is just the core nucleus of Helium atom (no electrons) 01 e beta particle is a fast moving electron 01 e positron, like a beta particle but has a + charge hv gamma is NOT a particle, just a very high frequency light wave H= 11 H= normal hydrogen atom (proton only) D = 21 H= deuterium- hydrogen atom + 1 extra neutron T = 31 H= tritium- hydrogen atom + 2 extra neutrons (by product of Uranium)

Conservation laws: (useful for balancing nuclear reactions) 1. Mass-energy 2. Charge 3. momentum 4. number of nucleons (protons or neutrons)

Possible Demos 1. Cloud chamber- see alpha tracks using dry ice cloud 2. Geiger counter- test common household items 3. Geiger counter- inverse square law, shielding, magnetic bending 4. Geiger counter- cosmic rays 3

Cliff notes: What is radioactivity, or radioactive decay? spontaneous emission of energy in form of particles or rays from an unstable nucleus What is ionizing radiation? Kicks out electrons, breaks chemical bonds. UV, x-rays, gamma rays, high energy particles What’s hot in my house?.......YOU are (by what you eat, inhale, and absorb) house (Radon), food(potassium), glowing watches(radium), smoke detectors (americium) orange fiesta ware (uranium), camping gas mantels (thorium), some paint (lead) How can you reduce the radiation? 1. Less time: reduce your exposure (typical 350 mrem/year) 2. More distance : inverse square law: 1/4 if double distance 3. use shielding: lead, water, graphite, boron, etc What types of radiation are emitted during radioactive decay? 1. Alpha (α) particle: large, slow, He nucleus, charge=2, bend w/magnet stop with just air or skin, ex: Pu-236, U-238, radium-226, radon-222. 2. Beta (β) particles: fast electrons, charge=-1, bend w/magnet, attacks bones stop w/thin wood,metal, ex: strontium-90, co-60, iodine-129, ce-137. 3. Gamma rays (γ) : high frequency photons, no charge, can’t bend w/magnet need thick lead/concrete to stop, emitted after initial  or β decay What is a half life? After time of one half life, half of the number of radioactive atoms have decayed or changed What is mass deficit, m?............................................(tougher math problems) m = difference in mass between original reactants and final product. m*c2= binding energy of a fused nucleus or m*c2 = KE of fission products (use atomic mass units “u” to make math easier) 4

What are the 3 types of Transmutations or nuclear reactions? 1.( Alpha: A parent nucleus decays into a lower atomic number daughter plus a high energy He nucleus of 2 protons and 2 neutrons (alpha particle)

A Z P------------------------

A-4 Z-2

Parent Mass ---------------------------



42 He

daughter mass

(note: Z drops by 2,A by 4) + energy of alpha

kinetic energy of alpha: KE= m*c2 , m = parent – daughter nuclear masses

2. ()Beta: Parent decays into a higher atomic number daughter plus a high energy electron (parent neutron daughter proton + electron)

A Z P------------------------

A Z+1


Parent Mass ---------------------------


0-1 e

daughter mass

(note: Z raised by 1,A same) + energy of electron

kinetic energy of electron: KE= m*c2 , m = parent mass – daughter atomic mass 3. ()Gamma: Parent in excited state relaxes to lower state of same element plus high energy light (gamma rays) are emitted 152 γ Dy* ----> 152Dy + γ decay A Z P*------------------------


Parent Mass ---------------------------



hf (note: same element afterwards)

daughter mass

+ energy of electron

energy of light: hf= Ef – Ei = 13.6ev/nf2 - 13.6/ni2 (electron drops, light emitted)


What is fusion? (mass of reactants= mass of product + binding energy of nucleus) two light nuclei combine to form a single heavier nucleus, and release high amounts of energy due to the fused product is less than the total mass of the starting nuclei. 2 H + 3H ----> 4He + n

Examples: Sun, H bomb, lab experiments Why so difficult? Protons in each nuclei repel another. Takes lots of energy to push them close enough to get the strong nuclear force to take over and attract them. Iron is naturally most stable nucleus-it takes supernova explosions to create bigger than iron! Fusion is the process that takes place in stars like our Sun. Whenever we feel the warmth of the Sun and see by its light, we are observing the products of fusion. We know that all life on Earth exists because the light generated by the Sun produces food and warms our planet. fusion is the basis for our life! What is fission? (mass of parent

=-mass of products + KE of products)

A heavy nucleus splits into two smaller nuclei, releasing giant amounts of energy since the sum masses of the lighter product nuclei is less than the mass of parent nucleus. U + n ----> 134Xe + 100Sr + 2n


Examples: first atomic bomb, explosive start of H bombs, nuclear reactors. Fission occurs because the two smaller nuclei have less internal electrostatic repulsion than one larger nucleus. So, once the larger nucleus can overcome the strong nuclear force which holds it together, it can fission. In fission the repulsive electrostatic force wins the "tug-of-war" against the strong attractive nuclear force and releases energy.


Fill in the blank notes:

1. Put the terms in the correct box (one box is totally empty!) terms: radio, UV, x-rays, visible, microwaves, alpha, beta, gamma Electromagnetic Radiation Nonionizing Radiation Ionizing Radiation

Particle Radiation

Radio,vis,micro Uv, xray,gamma


2. Fill in the missing boxes: (e= charge of an electron, u = atomic mass unit) symbol

Mass (u)

Mass (kg)

Mass (MeV)

Charge (e)












1.673 x10-27





-1 e


9.11 x10-31



H atom







He atom


2 He


6.64 x10-27



C atom

12 6C


1.99 x10-26



3. Compare the 3 types of decay by deciding what happens to the original parent nucleus decay

Z changes by

A changes by

What’s emitted





2 He





-1 e






Balance each decay reaction, write the type of decay in the box

has a good periodic table!

He, alpha



e, beta

89 0Ac, alpha




Balance: 1 box is for atomic mass, 2



box for atomic number, 3 box is for which element 239








Balance: 1 box is for atomic mass, 2





box for atomic number, 3 box is for which particle


Sample math problems: (use lots of sig figs and a calculator!) A. Converting mass to energy………….. or energy to mass

A mass can be described in kilograms, or atomic mass units that are amu’s or u’s. Thanks to Einstein’s relativity, mass is also a measure of energy. So, mass can also be measured in energy units! (nuclear masses are mega electron volts MeV)

1 u= 1.66054E-27Kg= 931.5MeV This is to say that it takes 931.5 MeV of energy to create the mass of 1u or 1.66054E-27Kg.

1. Prove using E= mc2 , that 1 atomic mass unit (1u) has an energy of 931.5 x 106 eV. m=1u= 1.66x10-27Kg E= mc2= 1.66x10-27Kg * (3x108)2 * 1eV/1.6x10-19J = 933.8MeV

2. How much energy is the conversion of one neutron to a proton as in beta decay (use 1proton =1.0073 u, 1 neutron = 1.0087u) (answer: 1.3041MeV) error, it’s neutron changing into a proton plus electron .0014u * 931.5MeV/u = 1.30141MeV

3. What would the kinetic energy of the electron be for problem #2? (1.69x1018m/s) 1 1 p------------------

1 0



0-1 e


Use KE= 1/2mv2 = 1.3x106 eV8 1.6x10-19J


B. Mass defect Problems Unlike chemical reactions, nuclear reactions change energy to mass and reverse. When parts are fused to together to make a new nucleus, there is mass loss. The nucleus weighs less than its parts! Some of the mass is “missing” or deficit. The mass is actually being stored as the energy it takes to hold it together, called the nuclear “binding energy”. Likewise, when the nucleus is fissioned apart, the new fragments have less mass than the original nucleus. This loss is mass is because the fragments are moving fast and high new energy, which was taken from their mass. All elements smaller than iron (z=42), can be pressure fused together and become hotter (like H + H = He in our Sun). Elements from Bi (=83) down to iron can be bombarded and fissioned apart with high kinetic energy fragments. Elements above Bi are unstable and naturally fission apart without any help. ** The difference in mass must be nuclear, not atomic which includes electrons! most tables (including appendix F in our book ) give atomic weights so you must account for electron mass by including electrons in both reactants and products or subtracting them out 4. What is the binding energy of the nucleus of carbon,


6 C,

whose mass = 12u.

Mass of 6 protons + mass of 6 neutrons = mass of carbon nucleus + binding energy

5. Tritium nucleus, 31H, is 2 neutrons and 1 proton stuck together. Tritium atom has an atomic mass of 3.016049 u (this includes mass of one electron!).

a. what is Tritium’s nuclear mass? (3.015500u)

b. What is that in MeV?

(2809 MeV)

c. What is the mass of the original 2 neutrons and 1 proton? (3.024606u)

d. How much mass is the Tritium nucleus missing? (.009106u)

e. What is the binding energy that holds the Tritium nucleus together? (8.482 MeV)


AP Questions

1. Consider the following nuclear fusion reaction that uses deuterium as fuel. 2001B7 3( 21 H) 42 He11H 01n a.

Determine the mass defect of a single reaction, given the following information. 2 1

H  2.0141u

4 2

He  4.0026u

1 1

H  1.0078u

1 0

n  1.0087u

Reactants = 6.0723 u, products (all 3) add up to 6.0191 u, So mass difference = .0532u b.

Determine the energy in joules released during a single fusion reaction. .0532*931.5MeV


The United States requires about 1020 J per year to meet its energy needs. How many deuterium atoms would be necessary to provide this magnitude of energy?

1020 / (0532*931.5MeV/3) since 3 deuteriums in above reaction


Assume that 0.015% of the hydrogen atoms in seawater (H20) are deuterium. The atomic mass number of oxygen is 16. About how many kilograms of seawater would be needed per year to provide the hydrogen fuel for fusion reactors to meet the energy needs of the United States?

1020 = x atoms * 1 water/2 atoms * .018kg * .015 solve for x


2. A lithium nucleus, while at rest, decays into a helium nucleus of rest mass 6.6483 x 10-27 kilogram and a proton of rest mass 1.6726 x 10-27 kilogram, as shown by the following reaction.( 1989B5) 5 3

Li 24He 11H

In this reaction, momentum and total energy are conserved. After the decay, the proton moves with a nonrelativistic speed of 1.95 x 107 m/s. a. Determine the kinetic energy of the proton. KE = 1/2mv2 = ½* 1.67x10-27 * (1.95x107) 2 = 3.18x10-13 J


(divide by 1.6x10-19 for eV)

Determine the speed of the helium nucleus.

initial momentum = 0 since at rest, so is final momentum so mv of helium = -mv of proton helium mass = 4u = 4x1.67x10-27 about ¼ as much if compare since masses: v = 1.95x107 * mass of proton/ mass of helium nucleus = 1.95x107 * (1.67 x 10-27)/6.648x10-27kg = 4.91x106


Determine the kinetic energy of the helium nucleus.

use KE= 1/2mv2 and last answer KE= ½ * 6.65x10-27 * 4.91x106 = 8.0 x 1014 J


Determine the mass that is transformed into kinetic energy in this decay.

use KE= mc2 but use KE of both part a and part c so m = total KE/c2 = (3.18x10-13 + 8.0 x10-14 )/( 3x108 )2 m= 4.42 x 10-30 kg


Determine the rest mass of the lithium nucleus.

Use Li mass = helium mass + H mass + KE of He (in u’s) + KE of H (in u’s) But last answer gave us the total KE in kg Li = 6.6483x10-27 + 1.67 x 10-27 + 4.42x10-30= 8.32 x 10-27kg , hot! (products always have more mass in all fission and fusion reactions)


3. An unstable nucleus that is initially at rest decays into a nucleus of fermium-252 containing 100 protons and 152 neutrons and an alpha particle that has a kinetic energy of 8.42 MeV. The atomic masses of helium-4 and fermium-252 are 4.00260 u and 252.08249 u, respectively. (1996Bp5) a. What is the atomic number of the original unstable nucleus? (102) 102





Fe +




Product mass = 252.08249 + 4.0060 = 256.08509

b. What is the velocity of the alpha particle? (Neglect relativistic effects for this calculation.) already given,just convert to MeV 8.42MeV = 8.42 x 106 * 1.6x10-19 J = 1.347 x 10-12 J Mass of alpha = 4u = 4*1.67x10-27kg but KE= 1/2mv2 Solve for v = 2.02 x 10 7 m/s (fast but not as fast as light)

c. Where does the kinetic energy of the alpha particle come from? Explain briefly. KE = mc2 (from difference in mass, some of reactants mass converted to energy)

d. Suppose that the fermium-252 nucleus could undergo a decay in which a - particle was produced. How would this affect the atomic number of the nucleus? Explain briefly. 100


Fe --



e +




increases by one, one of the neutron turns into proton + electron