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Based on this guide's real question bank — 142 practice questions across 9 units. Slide to match your situation.
Free-body diagram of a block on a frictionless incline: weight (mg) resolves into a component along the slope (mg sinθ) and a component into the surface (mg cosθ), balanced by the normal force.
Centripetal force always points toward the center of the circular path, perpendicular to the object's velocity, which is tangent to the circle.
Series circuit (same current everywhere, resistances add) vs parallel circuit (same voltage across each branch, resistances combine reciprocally).
A converging (convex) lens: an object beyond the focal point (F) forms a real, inverted image on the far side where refracted rays converge.
A runner moves 50 m east then 20 m west. What is the runner's displacement?
Displacement = 50 east − 20 east(since west is −) = 50 − 20 = 30 m east. Distance would be 70 m, but displacement is 30 m east.
What is the total distance traveled by the runner in the previous scenario?
Distance is the total path length: 50 m + 20 m = 70 m, regardless of direction.
Which quantity is a vector?
Displacement has both magnitude and direction, making it a vector. Distance, speed, and time are scalars.
On a position-time graph, the slope represents:
Slope of an x-t graph = Δx/Δt = velocity.
On a velocity-time graph, the area under the curve represents:
Area under a v-t graph = displacement (since Δx = v·t for each small interval).
An object has a positive velocity and a negative acceleration. The object is:
When velocity and acceleration have opposite signs, the object is slowing down (decelerating).
A car accelerates from rest at 4 m/s² for 5 seconds. What is its final velocity?
vf = vi + at = 0 + (4)(5) = 20 m/s.
A ball is thrown straight up. At the very top of its path, its acceleration is:
Gravity acts continuously; acceleration is always −g (downward) even at the peak where velocity is momentarily zero.
An object starts from rest and accelerates uniformly at 3 m/s² for 4 seconds. How far does it travel?
Δx = vi·t + ½at² = 0 + ½(3)(4²) = ½(3)(16) = 24 m.
A projectile is launched horizontally from a cliff. Compared to an object simply dropped from the same height at the same time, the projectile:
Horizontal and vertical motions are independent; both objects have the same initial vertical velocity (0) and the same vertical acceleration (g), so they fall for the same amount of time.
A ball is launched at 20 m/s at an angle of 30° above the horizontal. What is its initial vertical velocity component?
vyi = v sinθ = 20 sin30° = 20(0.5) = 10 m/s.
For maximum range on level ground (no air resistance), a projectile should be launched at an angle of:
Range is maximized at 45° for equal launch and landing heights, ignoring air resistance.
Which of the following can be true for an object with zero velocity?
An object can be momentarily at rest while still accelerating, such as a ball at the top of its toss, or a car just starting to move.
A car's velocity-time graph is a horizontal line above the time axis. This means the car has:
A horizontal (flat) line on a v-t graph means velocity isn't changing — constant velocity, zero acceleration.
An object's average speed over a trip is 20 m/s. Its average velocity for the same trip:
Average speed = total distance/time; average velocity = displacement/time. Since distance ≥ |displacement|, average speed ≥ |average velocity|.
A ball is dropped from rest and falls for 2.0 s. How far does it fall (use g=9.8 m/s²)?
Δx = ½gt² = ½(9.8)(2.0²) = ½(9.8)(4) = 19.6 m.
Which kinematic equation should be used if you know vi, a, and Δx, and want to find vf without knowing t?
vf² = vi² + 2aΔx is the only kinematic equation that omits time.
An object moves at constant velocity. What can you conclude about the net force acting on it?
Constant velocity means zero acceleration, so by Newton's Second Law, the net force must be zero.
A 10 kg object experiences a net force of 25 N. What is its acceleration?
a = Fnet/m = 25/10 = 2.5 m/s².
Which pair of forces is an example of a Newton's Third Law force pair?
Action-reaction pairs act on two DIFFERENT objects — the hammer pushes the nail, the nail pushes back on the hammer with equal and opposite force.
A book rests on a table. The normal force on the book is equal in magnitude to the book's weight. This is an example of:
Weight and normal force act on the SAME object (the book) and happen to balance since the book isn't accelerating vertically — NOT a third-law pair, which would require different objects.
What is the weight of a 5 kg mass on Earth (g = 9.8 m/s²)?
Fg = mg = (5)(9.8) = 49 N.
A box on a horizontal surface has a mass of 8 kg and a coefficient of kinetic friction of 0.3. What is the kinetic friction force (g=9.8 m/s²)?
FN = mg = (8)(9.8) = 78.4 N. fk = μkFN = (0.3)(78.4) = 23.5 N.
Which statement about mass and weight is correct?
Mass (kg) measures the amount of matter and doesn't change; weight (N) = mg depends on the local gravitational field.
A rope holds a 12 kg mass stationary, hanging vertically. What is the tension in the rope (g=9.8 m/s²)?
Since the mass is in equilibrium, tension equals weight: T = mg = (12)(9.8) = 117.6 N.
An astronaut has a mass of 70 kg on Earth. On the Moon, where gravity is about 1/6 of Earth's, the astronaut's mass is:
Mass does not change with location — only weight changes. The astronaut's mass remains 70 kg on the Moon.
Which of the following increases the maximum static friction force between two surfaces?
Maximum static friction fs,max = μsFN depends on the normal force (and μ), not on contact area or velocity.
A block sits on a frictionless incline at angle θ. The component of gravity acting parallel to the incline surface (down the slope) is:
The component of weight parallel to the incline is mg sinθ; the component perpendicular (balanced by normal force) is mg cosθ.
Two blocks are connected by a rope over a frictionless pulley. Which law explains why the same magnitude of acceleration applies to both blocks?
Because the rope doesn't stretch, both blocks must have the same speed and acceleration magnitude at all times — a constraint, not directly a Newton's law statement.
Which of these is NOT one of Newton's Laws of Motion?
'Energy cannot be created or destroyed' is the law of conservation of energy, not one of Newton's three laws of motion.
A 1000 kg car accelerates at 2 m/s². What net force is required?
Fnet = ma = (1000)(2) = 2000 N.
When you push against a wall, the wall pushes back on you with equal force. This is best explained by:
Newton's Third Law: for every action force, there's an equal and opposite reaction force.
An object is in equilibrium on an incline, held by a rope parallel to the incline. The tension in the rope is:
For equilibrium along the incline, tension must balance the component of gravity along the incline: T = mg sinθ.
Which best describes inertia?
Inertia is the tendency of matter to resist changes in velocity (both magnitude and direction); mass is the quantitative measure of inertia.
A 2 kg object moves at 5 m/s. What is its momentum?
p = mv = (2)(5) = 10 kg·m/s.
A 3 kg object experiences a net force of 6 N for 2 seconds. What is the impulse delivered?
J = FΔt = (6)(2) = 12 N·s.
Airbags reduce injury in car crashes primarily by:
For a fixed impulse (Δp), extending the time of impact reduces the average force (J=FΔt), which is how airbags reduce injury.
Two objects of equal mass moving in opposite directions with equal speed collide and stick together. What is their final velocity?
Total initial momentum = mv + m(−v) = 0, so by conservation of momentum, final momentum must also be zero, meaning they stop.
Which type of collision conserves both momentum AND kinetic energy?
Elastic collisions conserve both momentum and total kinetic energy; inelastic collisions conserve only momentum.
A 4 kg cart moving at 3 m/s collides and sticks with a stationary 2 kg cart. What is their common final velocity?
Conservation of momentum: (4)(3) + (2)(0) = (4+2)v → 12 = 6v → v = 2 m/s.
How much work is done by a 10 N force pushing an object 5 m in the direction of the force?
W = Fd cosθ = (10)(5)(cos0°) = 50 J.
A person carries a heavy bag horizontally at constant velocity across a room. How much work does the person do on the bag (ignoring the initial lift)?
The applied force (upward, to support the bag) is perpendicular to the horizontal displacement, so W = Fd cos90° = 0.
What is the kinetic energy of a 2 kg object moving at 6 m/s?
KE = ½mv² = ½(2)(6²) = ½(2)(36) = 36 J.
If the speed of an object doubles, its kinetic energy:
KE ∝ v², so doubling speed quadruples kinetic energy.
A 5 kg object is raised 3 m above the ground. What is its gravitational potential energy relative to the ground (g=9.8 m/s²)?
PE = mgh = (5)(9.8)(3) = 147 J.
A roller coaster car at the top of a hill has PE = 5000 J and KE = 0 (ignoring friction). What is its KE at the bottom of the hill if PE there is 0?
By conservation of mechanical energy, total energy stays constant: KEf = PEi − PEf + KEi = 5000 − 0 + 0 = 5000 J.
In a real roller coaster with friction, the total mechanical energy at the bottom of a hill compared to the top is:
Friction is a non-conservative force that removes mechanical energy from the system, converting it to heat and sound — total energy (including heat) is still conserved, but mechanical energy decreases.
Which quantity is conserved in ALL collisions, whether elastic or inelastic (assuming an isolated system)?
Momentum is always conserved in an isolated system's collisions; kinetic energy is only conserved in elastic collisions.
A spring with spring constant k=200 N/m is compressed 0.1 m. What is the elastic potential energy stored?
PEspring = ½kx² = ½(200)(0.1²) = ½(200)(0.01) = 1 J.
A car travels in a circle at constant speed. Which statement is true?
Even at constant speed, direction is continuously changing, producing centripetal acceleration directed toward the center.
A 1200 kg car rounds a curve of radius 50 m at 10 m/s. What centripetal force is required?
Fc = mv²/r = (1200)(10²)/50 = (1200)(100)/50 = 2400 N.
What force provides the centripetal force for a satellite orbiting Earth?
Gravity between the satellite and Earth supplies the necessary centripetal force for circular orbit.
If the distance between two masses is tripled, the gravitational force between them:
Gravity follows an inverse-square law: Fg ∝ 1/r². Tripling r reduces force to 1/3² = 1/9.
Two masses are doubled (both m1 and m2 double) while distance stays the same. The gravitational force between them becomes:
Fg ∝ m1m2, so doubling both masses multiplies the force by 2×2=4.
A ball on a string is swung in a horizontal circle. What provides the centripetal force?
Tension in the string pulls the ball toward the center, providing the centripetal force.
According to Kepler's Third Law, if planet A orbits at twice the radius of planet B (same central star), planet A's orbital period compared to planet B's is:
T² ∝ r³, so TA²/TB² = (2)³ = 8 → TA/TB = √8 = 2√2 ≈ 2.83.
An object moves in a circle at constant speed. Which of the following is constant?
Speed (magnitude of velocity) stays constant in uniform circular motion, but velocity direction and acceleration direction continuously change (though acceleration magnitude is constant, its direction always points to the center, which itself is a changing direction in space).
Universal gravitation constant G has units of:
From Fg = Gm1m2/r², G must have units of N·m²/kg² so the equation balances dimensionally.
A satellite orbits at a larger radius than another satellite around the same planet. Compared to the closer satellite, the farther one has:
Orbital speed v=√(Gm/r) decreases as r increases — farther satellites move slower.
Why is there no real outward force acting on a passenger in a car turning a corner (in an inertial frame)?
In an inertial reference frame, only a real inward (centripetal) net force acts; the sensation of being 'thrown outward' is simply the passenger's inertia resisting the change in direction.
A 500 kg satellite and a 1000 kg satellite orbit Earth at the same radius. Which has the greater orbital speed?
Orbital speed v=√(GMEarth/r) does not depend on the orbiting satellite's own mass — both have the same speed at the same radius.
Kepler's Second Law states that a planet sweeps out equal areas in equal times. This implies the planet moves:
To sweep equal areas in equal times while closer to the Sun (a shorter radius arm), the planet must move faster near perihelion.
What is the centripetal acceleration of an object moving at 4 m/s in a circle of radius 2 m?
ac = v²/r = (4²)/2 = 16/2 = 8 m/s².
A planet's orbit is best described by Kepler's First Law as:
Kepler's First Law: planetary orbits are ellipses with the Sun at one of the two foci.
If Earth's radius suddenly doubled with mass unchanged, the gravitational force on an object at the new surface would be:
Fg ∝ 1/r²; doubling the radius (distance to center) reduces surface gravity to 1/4.
A wave has a frequency of 5 Hz and a wavelength of 2 m. What is its speed?
v = fλ = (5)(2) = 10 m/s.
If the frequency of a wave increases while it stays in the same medium, its wavelength:
Since v=fλ and speed is fixed by the medium, increasing f must decrease λ proportionally.
Sound is best classified as a:
Sound is a longitudinal wave — particles vibrate parallel to the direction of wave travel, creating compressions and rarefactions.
Sound cannot travel through a vacuum because:
Sound is a mechanical wave requiring particles to transmit compressions and rarefactions; a vacuum has no particles.
Sound travels fastest through which medium?
Sound travels fastest in solids because particles are closest together and transmit vibrations most efficiently, slower in liquids, slowest in gases.
Two identical waves arrive perfectly in phase at the same point. This is an example of:
In-phase waves add their displacements together, producing a larger amplitude — constructive interference.
An ambulance siren sounds higher-pitched as it approaches you and lower-pitched as it drives away. This is:
The Doppler effect: the source moving toward you compresses wavefronts (higher perceived frequency); moving away stretches them (lower perceived frequency).
What actually happens to the siren's emitted frequency as the ambulance moves toward and then away from a stationary observer?
The source's actual emitted frequency never changes; only the frequency perceived by the observer shifts due to relative motion.
Which best describes amplitude?
Amplitude is the maximum displacement from equilibrium and relates to the energy/intensity (loudness for sound) carried by the wave.
A standing wave is formed by:
Standing waves result from the superposition of two identical waves traveling in opposite directions, creating fixed nodes and antinodes.
A wave's period is 0.25 s. What is its frequency?
f = 1/T = 1/0.25 = 4 Hz.
Which property of a sound wave corresponds to its perceived pitch?
Pitch corresponds directly to frequency — higher frequency sounds are perceived as higher pitch.
Points of maximum displacement in a standing wave are called:
Antinodes are points of maximum displacement; nodes are points of zero displacement.
Resonance occurs when:
Resonance is a dramatic amplitude increase that occurs when a driving frequency matches a system's natural frequency.
A wave's amplitude is doubled. Its wave speed:
Wave speed depends only on the properties of the medium, not amplitude or frequency.
Two point charges of +2 μC and +3 μC are separated by 0.1 m. What is the electric force between them (k=8.99×10⁹ N·m²/C²)?
Fe = kq1q2/r² = (8.99×10⁹)(2×10⁻⁶)(3×10⁻⁶)/(0.1²) = (8.99×10⁹)(6×10⁻¹²)/0.01 ≈ 5.39 N.
If the distance between two charges is halved, the electric force between them becomes:
Coulomb's law is inverse-square: halving r increases force by a factor of (1/0.5)²=4.
Electric field lines around an isolated positive charge point:
Field lines point away from positive charges (the direction a positive test charge would be pushed) and toward negative charges.
A resistor has V=12 V across it and carries I=3 A. What is its resistance?
R = V/I = 12/3 = 4 Ω.
Three 2 Ω resistors are connected in series. What is the total resistance?
Series resistances add directly: Rtotal = 2+2+2 = 6 Ω.
Three 6 Ω resistors are connected in parallel. What is the total resistance?
1/Rtotal = 1/6+1/6+1/6 = 3/6 = 1/2, so Rtotal = 2 Ω.
In a series circuit with two resistors, which quantity is the same through both resistors?
In a series circuit, there's only one path, so the current is identical through every component.
In a parallel circuit, which quantity is the same across every branch?
Each parallel branch connects across the same two nodes, so voltage is identical across all branches.
A circuit has a 12 V source and total resistance of 4 Ω. What is the total current?
I = V/R = 12/4 = 3 A.
A device draws 2 A at 120 V. What power does it consume?
P = IV = (2)(120) = 240 W.
If one bulb burns out (opens) in a series string of holiday lights, what happens to the rest of the string?
In a series circuit there's only one current path; if it's broken anywhere, no current flows anywhere in the loop.
If one branch fails (opens) in a parallel circuit, what happens to the other branches?
Parallel branches are independent paths; if one opens, current can still flow through the remaining branches.
Which of the following increases the resistance of a wire?
R = ρL/A — resistance increases directly with length and decreases with cross-sectional area.
What is the SI unit of electric charge?
The coulomb (C) is the SI unit of electric charge.
A charge of 4 C flows past a point in a wire in 2 seconds. What is the current?
I = q/t = 4/2 = 2 A.
Doubling the voltage across a fixed resistor does what to the power dissipated?
P = V²/R, so doubling V quadruples P (for constant R).
Which statement about magnetic poles is correct?
As with electric charges, like magnetic poles repel and opposite poles attract; monopoles have never been observed.
Outside a bar magnet, magnetic field lines point:
Outside the magnet, field lines emerge from the north pole and enter the south pole, forming closed loops through the magnet's interior.
A charged particle moves parallel to a magnetic field. What magnetic force does it experience?
F = qvB sinθ; when θ=0° (parallel), sinθ=0, so the force is zero.
A charged particle moves perpendicular to a magnetic field. What is the shape of its resulting path?
The magnetic force is always perpendicular to velocity, continuously changing direction without changing speed — producing uniform circular motion.
The magnetic force on a moving charge does what to its kinetic energy?
Since F is always perpendicular to v, it does no work on the charge, so kinetic energy (and speed) stays constant.
What is required to induce an EMF in a loop of wire via electromagnetic induction?
Faraday's Law requires a CHANGING magnetic flux — a constant field through a stationary loop induces nothing.
According to Lenz's Law, an induced current flows in a direction that:
Lenz's Law: induced current opposes the change in magnetic flux, consistent with conservation of energy.
A generator converts:
A generator uses mechanical motion (rotating a coil in a magnetic field) to induce an EMF — converting mechanical to electrical energy.
A motor converts:
A motor uses current in a magnetic field to produce a force (torque), converting electrical energy into mechanical motion.
A wire carrying current I=5 A, of length 0.4 m, sits perpendicular to a magnetic field of 0.2 T. What force does it experience?
F=BIL sinθ = (0.2)(5)(0.4)(sin90°) = 0.4 N.
Increasing the number of turns in a coil used for electromagnetic induction:
More turns means the changing flux links more loops, increasing the total induced EMF.
The direction of the magnetic field around a straight current-carrying wire is found using:
The right-hand rule: point the thumb along conventional current, and the curled fingers show the direction of the circular magnetic field.
A magnet is pushed into a stationary coil of wire, inducing a current. If the magnet is pushed in faster, the induced EMF:
Faster motion means a faster rate of change of flux, which increases the induced EMF (Faraday's Law).
Why do AC generators produce alternating (rather than direct) current?
As the coil rotates, the rate and direction of flux change through it varies sinusoidally, producing an alternating induced EMF.
Which of the following experiences zero magnetic force in a magnetic field?
Magnetic force depends on velocity (F=qvB sinθ); a stationary charge (v=0) experiences no magnetic force.
A light ray strikes a plane mirror at 30° from the normal. At what angle does it reflect?
Law of reflection: angle of incidence = angle of reflection, both measured from the normal, so it reflects at 30° from the normal.
A plane mirror image is:
A flat (plane) mirror always forms a virtual, upright, same-size image located as far behind the mirror as the object is in front.
Light travels from air (n=1.00) into glass (n=1.50). It will bend:
Light bends toward the normal when entering a medium with a higher index of refraction (denser, slower light speed).
Light in water (n=1.33) hits the water-air boundary at an angle greater than the critical angle. What happens?
Beyond the critical angle, going from a denser to less dense medium, total internal reflection occurs — no light exits.
Using Snell's Law, light passes from a medium with n1=1.5 into a medium with n2=1.0, hitting the boundary at 30° from the normal. Which best describes the refracted angle?
n1sinθ1=n2sinθ2 → since n2<n1, sinθ2 must be larger than sinθ1, so θ2>30° — light bends away from the normal entering a less dense medium.
A convex (converging) lens forms what kind of image when the object is placed beyond the focal point?
When do>f for a converging lens, light rays converge on the far side, forming a real, inverted image.
An object is placed inside the focal length of a convex lens (do<f). The resulting image is:
When the object is closer than the focal point, the lens acts as a magnifying glass, producing a virtual, upright, magnified image.
An object is placed 30 cm from a convex lens with a focal length of 10 cm. Using 1/f=1/do+1/di, what is the image distance?
1/di = 1/f − 1/do = 1/10 − 1/30 = 3/30 − 1/30 = 2/30 = 1/15, so di = 15 cm.
A convex mirror (like a car's passenger side mirror) always forms an image that is:
Convex (diverging) mirrors always produce virtual, upright, reduced images, giving a wider field of view.
Which type of lens or mirror can form a REAL image?
Only converging elements (convex lens, concave mirror) can produce real images, and only when the object is beyond the focal point.
What is the index of refraction of a medium in which light travels at 2.0×10⁸ m/s (c=3.0×10⁸ m/s)?
n = c/v = (3.0×10⁸)/(2.0×10⁸) = 1.5.
Which best explains why a straw appears bent at the water's surface when viewed from the side?
Refraction bends light rays as they cross the water-air boundary due to the change in speed, making the submerged part of the straw appear displaced/bent.
A magnification of m=−2 for an image means:
A negative m indicates an inverted image; the magnitude (2) means the image is twice the height of the object.
Diffuse reflection occurs because:
A rough surface reflects parallel incoming rays at many different angles (still following the law of reflection at each microscopic point), preventing a clear image from forming.
The critical angle for total internal reflection depends on:
sinθc = n2/n1, so the critical angle depends on the ratio of the refractive indices of the two media.
In the photoelectric effect, increasing the intensity of light above the threshold frequency mainly increases:
Intensity relates to the number of photons hitting the metal per second, which increases the number (rate) of ejected electrons, not their individual energy.
In the photoelectric effect, increasing the frequency of light (above threshold) mainly increases:
Each photon's energy is E=hf; higher frequency means each photon carries more energy, increasing the max KE of ejected electrons (KEmax=hf−W0).
A metal has a work function of 2.0 eV. Light with photon energy 3.0 eV strikes it. What is the maximum kinetic energy of an ejected electron?
KEmax = hf − W0 = 3.0 − 2.0 = 1.0 eV.
Light striking a metal below its threshold frequency, no matter how intense, will:
Below the threshold frequency, individual photons don't carry enough energy to overcome the work function, so no electrons are ejected regardless of intensity.
The de Broglie wavelength of a particle is given by:
De Broglie's relation: λ = h/p = h/(mv), describing the wave nature of matter.
Which experiment provides strong evidence for the wave nature of light?
Double-slit diffraction and interference patterns are classic evidence of light's wave nature; the photoelectric effect instead evidences light's particle nature.
In the Bohr model, an atom emits a photon when:
A photon is emitted when an electron transitions from a higher to a lower allowed energy level, releasing energy equal to the level difference.
Bright-line emission spectra are unique to each element because:
Each element has a distinct set of quantized energy levels, so the photon energies (and thus wavelengths) it can emit/absorb form a unique 'fingerprint.'
Which particle is emitted in alpha decay?
Alpha decay emits an alpha particle, which is a helium-4 nucleus (2 protons, 2 neutrons).
After an alpha decay, the mass number and atomic number of the parent nucleus change by:
Alpha decay removes 2 protons and 2 neutrons, so mass number decreases by 4 and atomic number decreases by 2.
Which type of radioactive decay is stopped by just a sheet of paper?
Alpha particles have the least penetrating power (but highest ionizing power) and are stopped by paper or skin.
Which type of radioactive decay requires lead or thick concrete to stop?
Gamma rays are high-energy photons with the greatest penetrating power, requiring dense shielding like lead or thick concrete.
A radioactive sample has a half-life of 4 days. After 12 days, what fraction of the original sample remains?
12 days = 3 half-lives, so the remaining fraction is (1/2)³ = 1/8.
Nuclear fusion, the process that powers the Sun, involves:
Fusion combines light nuclei (e.g., hydrogen into helium), releasing a large amount of energy — the process that powers stars.
According to mass-energy equivalence, a small amount of mass converted entirely to energy releases:
E=mc² shows that even a tiny mass corresponds to an enormous amount of energy because c² (≈9×10¹⁶ m²/s²) is such a large number.
Beta decay involves:
In beta-minus decay, a neutron converts to a proton and an electron (beta particle) is emitted; atomic number increases by 1, mass number stays the same.
| Constant | Symbol | Value |
|---|---|---|
| Acceleration due to gravity | g | 9.8 m/s² |
| Universal gravitation constant | G | 6.67×10⁻¹¹ N·m²/kg² |
| Coulomb's constant | k | 8.99×10⁹ N·m²/C² |
| Elementary charge | e | 1.6×10⁻¹⁹ C |
| Planck's constant | h | 6.63×10⁻³⁴ J·s |
| Speed of light in vacuum | c | 3.0×10⁸ m/s |
| Speed of sound in air (room temp) | v | ≈343 m/s |
| Decay Type | Emitted | Mass # Change | Atomic # Change | Penetration |
|---|---|---|---|---|
| Alpha (α) | ⁴₂He nucleus | −4 | −2 | Stopped by paper (least penetrating, most ionizing) |
| Beta⁻ (β⁻) | ⁰₋₁e (electron) | 0 | +1 | Stopped by aluminum |
| Positron (β⁺) | ⁰₊₁e | 0 | −1 | Stopped by aluminum |
| Gamma (γ) | ⁰₀γ (photon) | 0 | 0 | Needs lead/concrete (most penetrating, least ionizing) |
| # Half-Lives | Fraction Left | % Remaining | % Decayed |
|---|---|---|---|
| 0 | 1 | 100% | 0% |
| 1 | 1/2 | 50% | 50% |
| 2 | 1/4 | 25% | 75% |
| 3 | 1/8 | 12.5% | 87.5% |
| 4 | 1/16 | 6.25% | 93.75% |
| 5 | 1/32 | 3.125% | 96.875% |
| Property | Series | Parallel |
|---|---|---|
| Current | Same through every component | Divides among branches |
| Voltage | Divides across components | Same across every branch |
| Total resistance | Rtotal = R1+R2+... | 1/Rtotal = 1/R1+1/R2+... (< smallest R) |
| If one component fails (opens) | Entire circuit stops | Other branches keep working |
| Region | Relative Wavelength | Relative Frequency/Energy |
|---|---|---|
| Radio | Longest | Lowest |
| Microwave | Long | Low |
| Infrared | Medium-long | Medium-low |
| Visible (ROYGBIV) | Medium | Medium |
| Ultraviolet | Medium-short | Medium-high |
| X-ray | Short | High |
| Gamma | Shortest | Highest |