Download AP Physics B Exam Cram Sheet - Mater Academy Lakes High School

AP Physics B Exam Cram Sheet (Ver. 4.01)
General Reminders
1. Look elsewhere for most of the equations, and remember: concepts come before the equations, not the other way
around.
2. “Normal” means perpendicular. Think about that for normal forces and the normal line in optics.
3. Choose a coordinate system that best suits Newton’s Laws. Try and get one of the axes to be so that F = 0 in that
direction. Otherwise, use Fx = ax, and Fy = ay, and aresultant = vector sum of the components.
4. For FR problems that require a solution in terms of given variables, use the variables given, not your own.
5. For FR problems, show all work (including verbalizing your thought processes in arriving at a deduction or
assumption).
6. Work done by a force is ALWAYS POSITIVE if the force and the direction the force goes are in the same direction.
7. We’ve tried a lot of different problems, but a favorite tactic of AP test writers is to take a conventional problem and
have students work it backwards.
8. Remember the things that are conserved: Mass and energy, linear momentum, angular momentum, electric charge.
9. With regard to forces, if it isn’t inside the nucleus (i.e. strong or weak) any force has to be electromagnetic or
gravitational.
10. ANY time spent studying is NOT time wasted… Take advantage of the time you have. On the other hand, don’t wait
until the last minute. If you could learn this all in one month, we’d have been reviewing for the exam since September.
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Mechanics
The slope of a position (distance) time graph is velocity (speed).
The slope of a velocity time graph is acceleration.
The direction an object accelerates is not necessarily the same direction it moves.
If acceleration and velocity and parallel, the object speeds up; antiparallel, slow down. Right angles, circular constant
speed. Anything else is some kind of curved path.
Parabolas on position-time graphs mean non-zero-slope straight lines on velocity-time graphs which mean zero-slope
(horizontal) lines on acceleration-time graphs.
Area under a velocity time graph is displacement (change in position). Areas below the time axis represent negative
displacements.
As a falling object approaches terminal velocity, speed increases and acceleration decreases.
Newton’s 1st or 2nd Law always applies. Newton’s 3rd Law always applies.
If the object is at rest or moving at a constant velocity, N1 applies. Otherwise N2 applies.
If an object is moving in a curve, there must be a net force towards the inside of the curve.
v2
If an object is moving in a circle, there must be a component of the net force towards the center equal to F  m .
r
The centripetal force is always a force easily identified (or the component of one…), e.g. friction, tension,
gravity, normal, or combinations.
The only force on any projectile (neglecting air friction) is the projectile’s weight (directed downwards).
A ball rolled off a horizontal table will take the same amount of time to hit the ground as another dropped from the
same height.
The tension in a rope holding an object in equilibrium is equal to the weight of the object. If the object is accelerating
upwards, T > mg. If the object is accelerating downwards, T < mg.
The angle of an inclined plane is the same as the angle between the line of weight of the object on the incline and the
normal line.
17. Static friction is a range of values such that 0  f s   N . Kinetic (sliding) friction is just f k   N .
18. The mass of a satellite doesn’t matter. The only thing that matters is the mass of the thing being orbited and the orbital
radius.
19. Geosynchronous orbit is approximately 22,300 mi. above the earth’s surface on the equatorial plane.
20. The closer a satellite is to what it orbits, the faster its orbital speed.
21. For satellites, the centripetal force is gravity: F 
GMm
mv 2

(assuming the orbit is circular and M >>> m).
r2
r
22. For satellites and planets, angular momentum (L = mvr) is always conserved (in the absence of any outside
forces/torques). In other words, the closer a planet is to the sun, the faster it goes.
23. The paths of planets and satellites are approximately circular, but are actually elliptical.
24. The gravitational force (and the resulting acceleration) due to a planet varies directly with the distance from the center
of the planet when the object is INSIDE the planet.
25. The gravitational force (and the resulting acceleration) due to a planet varies inversely with the square of the distance
from the center of the planet when the object is outside the planet.
26. A planet’s gravitational field is greatest at its surface (assuming it’s spherical).
27. A planet’s measured gravitational field is less at the equator than at the poles due to the planet’s rotation.
28. The tension in a string holding up an object is not always equal to the object’s weight.
29. The normal force exerted on an object (even on a horizontal surface) is not always equal to the object’s weight.
30. The direction an object will go is the same as the direction of the unbalanced force that makes it go, only if the initial
speed is zero.
31. For (modified) Atwood’s machines, consider a general direction for the acceleration, even if it’s not obvious.
32. Conical pendulums: Ty = mg, Tx = mv2/r.
33. In N3, the reaction force is always the same kind of force as the first one (the reaction to a frictional force is another
frictional force, the reaction to a gravitational force is another gravitational force).
34. The Law of Conservation of Momentum is based on the action-reaction pair of forces in Newton’s 3rd Law.
35. If conservative forces are the only forces doing work, mechanical energy is conserved.
36. Work done by conservative forces is path independent.
37. Power is the time rate of change of work or energy, but it can also be calculated using force  speed.
38. spring : pendulum :: spring constant : gravity :: mass attached : length.
39. If a mass on a spring hangs at rest a distance d, it will fall a distance 2d (measured from where the spring has no
potential energy).
40. In a collision between massive particles, momentum is ALWAYS conserved.
41. “Inelastic collisions” mean kinetic energy is not conserved.
42. “Completely inelastic” only means the objects stick together, not that all energy is lost (although some must be lost or
gained – hence the term “inelastic”).
43. “Perfectly elastic” means kinetic energy is conserved.
44. The first step in any torque problem is to determine the point about which torques are calculated.
45. The work done by any centripetal force is always zero.
46. The mass of a pendulum doesn’t matter.
47. If an object strikes a surface, the normal force exerted on the object must include the force required to change the
object’s momentum.
48. Normal forces generally don’t do work.
49. If two objects with mass collide, you MUST use momentum conservation at some point.
50. Consider variations on the ballistic pendulum (e.g. 1995:1).
51. The area under a force-position (displacement) graph is work (energy).
52. The work done in stopping an object is equal to its initial kinetic energy (likewise, the work done in getting an object
up to speed is equal to its final kinetic energy).
53. In any before-after situation, if there is a change in kinetic energy, work must have been done.
54. Conservative fields are defined by potential energy functions (gravitational, elastic, electric). Watch out for the
hypothetical conservative field.
55. Potential energy is generally considered an assigned (arbitrary) energy due to position.
56. If you’re being asked for the kinetic energy of an object, don’t be too quick to use K  12 mv unless the mass and
speed are obvious and available. Think about using work-energy considerations.
2
57. Also, don’t forget the relation between kinetic energy and momentum: K 
v v uv
58.
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60.
61.
p2
2m
.
Torque is a vector cross product.   r  F  rF sin  .
Work is a dot scalar product. W  F gx  F x cos  .
An object can be in translational or rotational equilibrium or both or neither.
Work done by kinetic friction is negative.
62. This equation goes a long way:   2 f 
2
T

k
m

g
l
; the first part is applicable to waves.
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Fluids & Thermodynamics
Pascal’s Law: Changes in pressure in an enclosed fluid is transmitted equally throughout the fluid.
Archimedes’ Principle: Objects displace their own volume when placed in a fluid, and the buoyant force is equal to the
weight of the displaced fluid.
Objects sink in a fluid that has a lower density.
An ideal fluid is incompressible and has no viscosity.
In steady flow, the rate of mass movement is constant throughout the tube (think continuity equation).
Bernoulli’s equation looks like one of energy conservation because that’s what it is.
The speed of efflux is the same as the speed a body would acquire in freefalling through the same height, i.e.
v  2 gh .
8. Gauge pressure is the excess above atmospheric pressure,
i.e. absolute pressure = atmospheric pressure + gauge pressure.
9. Fluids like to go from high pressure to low pressure.
10. Pressure increases underwater 1 atmosphere for about every 10 meters.
11. The pressure exerted by a fluid on a surface is normal to the surface.
12. p  p0   gh is a linear equation (p as a function of h; the slope is g, the intercept is p0.)
13. Most materials expand upon heating. Water is a weird exception near 4C.
14. The area under a pV graph is work done BY the gas.
15. Isothermal means constant T (T=0). Isobaric means constant p (p=0). Isometric means constant V (V=0).
Adiabatic means no heat is transferred (Q=0).
16. U = 0 for any cyclic process.
17. pV cycles that go clockwise are engines. CCW = refrigerators.
18. Carnot cycles involve only isothermal and adiabatic processes, and the only thing that determines the efficiency is the
temperatures of the reservoirs.
19. On a pV diagram, inner isotherms are colder.
20. U (for a fixed amount of ideal gas) for any TD process depends only on T, although it can be calculated a number of
different ways. Likewise, the internal energy U of a fixed amount of an ideal gas depends only on its temperature.
21. Watch out for all the quantities associated with pV diagrams (states and processes) and realize that there are usually
many ways of arriving at the same results.
22. Once you commit pV  nRT  23 U to memory, a lot of other stuff falls into place.
23. The internal energy of an ideal gas is considered to be all kinetic energy, for calculation purposes. It is defined as the
total kinetic and potential energies of all the particles, though.
24. The Universal Gas Constant (R) is for moles, and Boltzmann’s Constant (kb) is for molecules. The ratio of R to kb is
Avogadro’s Number.
25. For kinetic theory stuff, watch out whether you’re solving for an individual molecule, a mole, or the entire sample.
26. Watch out for SI units! (most molar masses are given in gmol-1… which ain’t SI)
27. Any time you see a T by itself in an equation, use Kelvins. T can be Kelvins or C.
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Charged Surfaces and Spheres (Electrostatics – Gauss’ Law)
Excess charge resides on the outer surface of a conductor.
The field anywhere inside a conductor in electrostatic equilibrium is zero.
The surface of any charged conductor in electrostatic equilibrium is a surface of equipotential.
The electric potential on the surface of conducting sphere is inversely proportional to radius of the sphere. (i.e. given
the same quantity of charge, surfaces of smaller spheres are at a higher quantity of potential).
On irregularly shaped conductors, the surface charge density (and therefore the field and potential) is higher at
locations where the radius of curvature is smallest (like ends of lightning rods and golf clubs).
If two charged objects are connected by a conductor, the difference in potential will cause the charges to move until the
potentials are the same. And don’t forget, positive charges move from high to low potential – negative charges (e.g.
electrons) go from low to high potential.
7. For a conducting sphere of radius R ,
The electric field at the surface is E 
kQ
.
R2
The field anywhere inside the sphere is 0.
The field at a distance r away from the center of the sphere (where r  R ) is E 
kQ
r2
.
8. For the same conducting sphere,
The potential at the surface is V 
kQ
.
R
The potential anywhere inside the sphere is the same as at the surface, otherwise there would be a difference
in potential and therefore an electric field that is  0.
kQ
The potential at a distance r away from the center of the sphere (where r  R ) is V 
.
r
9. For an insulating sphere of uniform charge density, the field inside the sphere varies directly with the distance from
the center (just like gravitational fields inside the earth). Outside it’s like the case above.
Electricity & Magnetism
1. Almost everything in electrostatics can be derived from Coulomb’s Law F 

Ñ

Gauss’ Law for electricity:  E  dA =
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12.
q enc
0
kqq 
r2
which in turn can be derived from
.
Remember to distinguish between what causes a field and what a field does to a charged particle.
For our purposes, an object cannot be affected by its own field.
Fields exert forces. It’s what they do. It’s what they are. It’s their job.
Forces and potential energies are associated with particles. Fields and potentials are associated with points in space.
Positive charges want to go from regions of high potential to regions of low potential.
The direction of electric field is the direction of the force the field exerts on a positive charge. Or, the direction of
electric field is the same as the direction from high potential to low potential.
Lines of equipotential are perpendicular to electric field lines.
Fields and forces are vectors. They have directions according to their signs. Strip the signs and do vector math.
Potential and potential energy are scalars. Keep the signs (!) and just add.
For potential and potential energy, the reference point (where V = 0 and U = 0) is r   .
For the motion of a charged particle in an electric field, use the system of equations for constant acceleration that we
used for projectiles.
13. Don’t use V  Ed for point charges and don’t use V 
kq
or E 
kq
for parallel plates.
r
r2
14. If you have to do vector math to find the field due to several charges at a given point, the total force on a charge placed
on that point is simply F  q(E ) . Don’t do vector math twice for the same concept.
15. No work is done in moving a charged object along a line or surface of equipotential. (W=qV=0)
16. One electronvolt is the amount of energy an electron (or a proton) acquires when it is accelerated from rest through a
difference in potential of one volt. (W=qV=K).
17. The capacitance of a system of parallel plates depends only on the physical characteristics of the capacitor (i.e. surface
area, plate separation, dielectric material).
18. The slope of a charge-voltage graph for a capacitor is its capacitance.
19. The area under a charge-voltage graph is work required to charge the cap = energy stored.
20. Capacitors charge by induction (charging by proximity as opposed to contact).
21. A capacitor always connected to a battery will have a constant voltage. A capacitor charged and then disconnected
from the battery will have a constant charge.
22. Capacitors take time to charge and discharge. As a capacitor is charging, the voltage builds up as the current through
the wires (connecting the cap to the battery) drops.
series
total
charge/current
voltage
parallel
Capacitors
inverse thing
Resistors
add ‘em up
Capacitors
add ‘em up
Resistors
inverse thing
same
same
Q=CV (adds up)
I = R/V (adds up)
V=Q/C (adds up)
V=IR (adds up)
same
same
23. The direction of conventional current is the way positive charges go in a circuit.
24. Resistivity is a general characteristic of a material (e.g. copper) while resistance is a specific characteristic of a sample
of a material (e.g. 2 ft of 14 gauge copper wire).
25. Resistance is proportional to length and inversely proportional to cross-sectional area.
26. Superconductors have zero resistance when cooled below a critical temperature (different for different materials).
Currently, high temperature superconductors – ceramics mostly - have critical temperatures of around 100 K).
27. Stuff that requires a lot of heat uses the most electricity.
28. The equivalent resistance of any two identical resistors in parallel is half of either resistor. (e.g. 2 8- resistors in
parallel give an eq. R = 4-).
29. The equivalent resistance of any number of resistors in parallel is always less than that of the smallest resistor.
30. Kirchhoff’s Loop Rule (V = 0) is an expression of conservation of energy (per unit charge).
31. Kirchhoff’s Point Rule (I = 0) is an expression of conservation of electric charge (per unit time).
32. If you must use the Loop Rule or the Point Rule, remember your sign conventions for emf’s and IR’s in a loop. The
convention for the Point Rule is too obvious to print.
33. Voltmeters have a high resistance (to keep from drawing current) and are wired in parallel (because voltage is the same
in parallel).
34. Ammeters have a low resistance (to keep from reducing the current) and are wired in series (because current is the
same in series).
35. A light bulb lights up because of current. The more current, the brighter it is. Generally, we’ll treat the resistance of the
light bulb as ohmic (i.e. constant – it follows Ohm’s Law), although actually most metallic conductors increase in
resistance when heated.
36. Moving electric charges (current) creates magnetic field (Oersted), but a changing magnetic field creates an electric
current (Faraday).
v
v
37. The motion of a charged particle in a magnetic field can either be a circle (when v  B …   90 ), a straight line
v v
(when v P B …   0 ) or a helix (when 0    90 ).
38. Magnetic fields don’t do work on charged particles moving through the field because the force is always perpendicular
to the velocity.
39. The force of a magnetic field on a charged particle moving through the field is always perpendicular to the plane
formed by the field and velocity vectors (rays).
40. Magnetic force on a charge depends on the quantity of charge and strength of the field (like electric fields) but also on
the magnitude and direction of the velocity of the particle.
41. Magnetic force on a charged particle is at its maximum when the field and velocity vectors are at right angles. The
force is at a minimum (0) when the field and velocity vectors are parallel or antiparallel.
42. Mass spectrometers have two ways of injecting particles:
a. Accelerate the particles through a difference in electric potential, so W  qV  12 mv .
2
b. Pass the particles through a velocity selector, which crosses a magnetic field with an electric field, yielding zero
E
net force for particles moving a certain speed, qvB  qE , so v  .
B
43. Don’t forget all of your right hand rules, and don’t use your left hand…

v v

44. Magnetic flux   B  A  BA cos  is a dot-scalar product.
45. There are two general situations where Faraday’s Law applies:
a. An emf is induced by magnetic forces on charges when a conductor moves through a constant magnetic field
 BA B (x  l )


 vBl )
(think of this as emf 
t
t
t


b. An emf is induced in a stationary loop by a changing magnetic field  emf 
B  A

 
.
t
t 
46. Bottom line: if you want to know if a current is being induced in a loop, ask yourself if the flux through the loop is
being changed. If the flux doesn’t change, there’s no induced emf.
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Waves & Optics
Mechanical waves can be longitudinal (displacement is parallel to motion) or transverse (displacement is perpendicular
to motion). EM waves are treated as transverse waves.
Sound is a longitudinal wave.
On a string (or in a pipe) where a standing wave occurs, the number of loops (antinodes) is the number of the harmonic.
The open end of a pipe is always a pressure node because it stays at atmospheric pressure.
Frequency : pitch :: amplitude : loudness :: harmonic content : timbre (tone quality).
The speed of a wave depends only on the properties of the medium. This is true for mechanical as well as EM waves.
Wave energy is generally directly associated with amplitude (do not confuse this with quantum ideas…).
Properties of waves include refraction, superposition & interference, and diffraction. Waves also reflect, but so do
particles.
Real images are formed by the convergence of light rays (where the light goes). Virtual images look like they are where
the light came from.
Lenses work because of refraction. The greater the index of refraction of the lens the more light will change direction
(bend), and the closer the focal point is to the lens.
For lenses, there are two focal points, one on each side. For mirrors, there is only focal point halfway between the
mirror and the center of curvature.
Different wavelengths of light have different indices of refraction in a given medium. (Generally, violet has a higher
index of refraction than red.)
When a wave refracts (goes from one medium to another) its speed and wavelength change (proportionally) and
frequency remains constant.
For refraction, a wave (ray) is closer to the normal in the medium with the higher index of refraction (remember the
bird and the fish).
Covering up a portion of a lens or mirror will only reduce the amount of light that will form the image. It won’t change
the position or size.
Index of refraction doesn’t have anything to do with mirrors.
Index of refraction has everything to do with lenses.
Converging – light bends toward the axis
lens: thicker in the middle
mirror: inside of curve
positive focal length
real & virtual images
real images when object is outside the focal pt.
virtual images when object is inside focal pt.
virtual images are always larger than the object
real images are smaller when object is further than 2f;
larger when object is between 2f and f.
real images are inverted
real images have to be projected (because light
actually converges on the screen)
Diverging – light bends away from the axis
lens: thinner in the middle
mirror: outside of curve
negative focal length
virtual images only
image is always closer than the object
image is always inside the focal point
images are always smaller than object
virtual images are erect
virtual images are not projected
18. Waves in phase are said to be coherent.
19. Interference patterns due to single slit, double slit or multiple slit (grating) setups always have a central maximum.
Rm
and m  d sin  are for maximum constructive interference for double or multiple slits.
d
The equations are for complete destructive interference for single slit.
20. The equations y 
21. The equation y 
22.
23.
24.
25.
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4.
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8.
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19.
Rm


is derived using the small angle approximation sin   tan  ,  tan  
y
m 
; sin  
;
R
d 
d
m


d sin  is an approximation assuming the rays leaving the openings are all parallel. But it’s close
for that matter,
enough to work…
In thin film interference, the thickness of the film is half of the path difference.
When a light wave strikes a boundary that has a higher index of refraction, it flips 180 out of phase upon reflection.
In thin film interference, figure out what the relative phase difference is between the reflected first ray and the reflected
refracted ray (!). Then figure out which condition you want (constructive/destructive interference).
In thin film interference, the wavelength of the reflected refracted ray is different in film than outside the film.
Modern Physics
Blackbody radiators are perfect radiators in that they absorb all incident radiation; therefore the only radiation coming
from a blackbody is radiation (a continuous spectrum) by virtue of its temperature. The higher the temperature, the
higher the frequency of the peak wavelength. (Red = cool; blue = hot)
The photoelectric effect (first observed by Hertz and later explained by Einstein) treats light as a particle (quantum or
photon) instead of a wave.
Photons interact with electrons on a one-to-one basis.
When photons interact with electrons, energy and momentum is conserved. (In the photoelectric effect, we don’t worry
about momentum – only energy).
The work function of a metal is a characteristic of the metal, and it’s the minimum (threshold) energy needed to eject
an electron from the metal (“tax”).
The work function energy for a metal is equal to the threshold energy of the incident radiation.
In the photoelectric effect, higher intensity of light just means more photons and therefore more electrons (and more
current), not faster electrons.
The only way to get faster electrons (more kinetic energy) in the photoelectric effect is to increase the frequency
(decrease the wavelength).
The slopes of all lines on a photoelectric effect graph are parallel. Different lines represent different materials with
different work functions. But they all have the same slope (related to Planck’s constant).
The vertical axis on a photoelectric effect graph is energy or voltage (energy/charge, potential, stopping potential, they
all mean basically the same thing… and watch for units). The horizontal axis MUST be frequency. Watch your units
when calculating slope.
The stopping potential in a photoelectric effect circuit is the amount of voltage you have to apply to stop the current
created by the photons. A stopping potential of 3 V means each electron has a kinetic energy of 3 eV (And the incident
photons have to be more than that in order to pay tax).
X-ray production is the photoelectric effect in reverse, without the work function (it’s negligible).
In either X-ray production or the photoelectric effect, it’s a lot easier to use electronvolts (eV) but watch your units.
Electronvolt is not SI for energy. (1 eV = 1.6  10-19 C  1 V = 1.6  10-19 J)
If you’re asked for a number of electrons or photons, remember they’re quantized. You can’t have fractions of electrons
or photons.
The Compton effect is a 2-D perfectly elastic collision between a photon and an at-rest electron. Energy and
momentum are conserved, which means the initial photon gives up some of its energy to the electron.
The photoelectric effect, X-ray production, and Compton scattering are all about energy conservation among photons
and electrons.
All photons go light speed. (Sorry, I had to say that at some time…)
de Broglie said if light can act like a particle, why can’t a particle act like a wave? Particles can have wavelengths…
Davisson and Germer verified it by bouncing electrons off a nickel surface and observing interference (diffraction)
patterns consistent with de Broglie’s equation.
J.J. Thomson discovered the electron in 1897 in experiments with a cathode ray tube and calculated the e/m ratio.
20. Rutherford did the gold foil thing in 1908 which was all about interactions of charged particles (helium nuclei
interacting with gold nuclei).
21. Line spectra are what caused Bohr to modify Rutherford’s planetary model of the atom by adding specific energy
levels. Electrons moving from level to level correspond to an energy difference equal to the energy of a photon.
22. Emission spectra are photons leaving the atom as electrons come down energy levels.
23. Absorption spectra are photons being absorbed as electrons move up energy levels from the ground state.
24. The most famous set of spectral lines is the Balmer series, where excited electrons come down to the 2nd energy level.
The emitted photons are in the visible light range.
25. The bigger the jump between energy levels, the more energy associated with the photons, the higher the frequency and
the shorter the wavelength.
26. The absorption of photons to move from the ground state to a higher state must be the exact energy and frequency. As
the bus says, “Exact change only”, unless you want to ionize the atom.
27. The ionization energy of an atom is equal to its ground state energy (e.g. the ground state of hydrogen is -13.6 eV,
which means a photon of minimum energy 13.6 eV will ionize the atom. Any more energy than that the electron gets to
keep as kinetic energy).
28. For our purposes, absorption by electrons will be from the ground state only.
29. Emission, on the other hand, can be from any excited level to any lower level.
30. Don’t mistake a list of absorption photon energies for the energy levels of the atom. If the absorption spectrum
consists of 5 eV, 7 eV, and 8 eV with an ionization energy of 11 eV, that means the atom will have a ground state
energy of –11 eV, and the 2nd, 3rd, and 4th energy levels will be –6 eV, -4 eV, and -3 eV, respectively.
31. The atomic number Z is the charge number (or number of protons). The mass number A is the total number of particles
in the nucleus. The atomic mass of an atom is the mass relative to 12C whose mass is defined to be exactly 12.000… u.
12
A
Nuclear notation for isotope X-A is Z X (e.g. C-12 is 6 C ).
32.
33.
34.
35.
36.
37.
1 atomic mass unit corresponds to an energy of about 931.5 MeV.
E = mc2. (It’s not just a good idea, it’s the law.)
Neutrons are slightly more massive than protons, and both are about 2000 more massive than electrons.
Atomic diameters are on the order of angstroms. (1 Å = 10-10 m = 0.1 nm)
Alpha particles are helium nuclei, beta particles are electrons, and gamma “particles” are photons.
Positrons are antiparticles to electrons; positrons and electrons totally annihilate each other on a one-to-one basis,
producing two 0.511 MeV photons traveling away from each other.
38. The mass of a nucleus is ALWAYS less than the sum of the masses of the nucleons. The difference in mass is the
nuclear binding energy associated with the strong force.
39. The only isotope with an atomic mass that is a whole number is Carbon-12, and that’s a definition.
40. In any nuclear reaction, electric charge is conserved.
41. In alpha decay, the mass number drops by 4 and the atomic number drops by 2.

A
Z
X  24 He 
A-4
Z-2
X

42. In beta- decay, the mass number remains the same and the atomic number increases by 1 (A neutron turns into a proton)
A
X  01 e  Z+1A X
Z


43. In any nuclear process the total rest mass decreases, corresponding to the energy released in the process.
44. Fission involves the splitting of heavy nuclei, like 238U. Neutrons are required for this particular process, which yields 2
or 3 more neutrons, depending on the products (which could be almost anything Uranium splits into 2 sort of
evenly…).
45. Fusion generally involves the combining of small nuclei (like hydrogen isotopes) to get heavier nuclei (like helium
isotopes).
46. Fusion releases way more energy than fission, produces little or no radioactive waste by-products, and is much more
efficient than fission. However right now it’s too hot to contain for long periods of time.
47. There are no such things as flux capacitors, dilithium crystals, matter-antimatter containment fields, or warp drives
(yet).