Chapter 10 - Creating Models

Question 1

Why are some atoms radioactive?

Answer 1

If an atom has too many neutrons, not enough neutrons or too much energy it will be unstable.

Unstable atoms break down by releasing energy and/or particles to reach a stable form.

Question 2

What do we mean by ‘radioactive decay is a random process”

Answer 2

Random:

- Cannot tell when any ONE atom will decay or WHICH atom in a sample will decay next.

Question 3

How does a model help to explain decay?

Answer 3

You cannot predict the decay of an individual atom but with a large enough sample of unstable atoms, the overall behaviour shows a pattern.

Thus, you can predict how many atoms will decay in a given time.

Question 4

What is the activity of a sample?

Answer 4

Number of unstable atoms that decay each second.

Question 5

What does the decay constant represent?

Answer 5

The probability that any particular nucleus will decay in a given unit of time.

(measures how quickly an isotope decays)

Bigger the decay constant, more likely decay is and thus faster rate of decay

Question 6

Unit of decay constant

Answer 6

s^-1

Question 7

The activity of a sample is proportional to…

Answer 7

The size of the sample.

As atoms decay, sample size gets smaller and thus activity falls.

Question 8

Activity

Answer 8

Decay constant x N

A = λN

Question 9

What is activity measured in?

Answer 9

Becquerels:

1 Bq = 1 decay per second

Question 10

What is half life?

Answer 10

The average time it takes for the number of undecayed atoms to halve.

Question 11

Half life equation:

Answer 11

T = ln 2 / λ

Question 12

Decay equation

Answer 12

N = N0 e ^ - λt

Question 13

What are capacitors?

Answer 13

Things that store electrical charge and energy.

Question 14

What is capacitance?

Answer 14

A measure of the quantity of charge a capacitor can hold.

Defined as amount of charge stored per volt.

Question 15

How does a capacitor store charge?

Answer 15

When a power source pumps electrons from the positive plate to the negative plate.

Question 16

Capacitance

Answer 16

C = Q/V

in farads (F) where 1 farad = 1 CV^-1

Question 17

How can you find the energy stored by a capacitor?

Answer 17

From the area under a graph of p.d against charge stored.

Question 18

Energy of a capacitor

Answer 18

E = 1/2 QV

E = 1/2 CV^2

Question 19

What happens when a capacitor is connected to a battery?

Answer 19

Current flows around the circuit until the capacitor is fully charged then stops.

When the p.d across the capacitor is equal to the p.d across the battery, current falls to zero and capacitor is fully charged.

Question 20

Why does current reduce?

Answer 20

Initially the current is high but as charge builds up on the plates, electric repulsion makes it more difficult for electrons to be deposited.

Question 21

What happens when a charged capacitor is connected across a resistor?

Answer 21

The p.d drives a current through the circuit.

Question 22

What happens when the power source is removed from charging capacitor?

Answer 22

Capacitor discharges, acting as a battery sending charge as current through load.

Question 23

What are the 2 things that affect the time it takes for charge/discharge?

Answer 23

1. Capacitance affects the amount of charge that can be transferred at a given voltage.
2. Resistance affects th current.

Question 24

Charge equation/Voltage equation

Answer 24

Q = Q0 e ^ -t/RC

Same for voltage and current.

Question 25

What is the time constant.

Answer 25

The time constant RC is the time taken for the charge on a discharging capacitor to fall to 37% of the original charge.

Or for charge of charging capacitor to rise to 63% of original charge.

Question 26

What happens with a large capacitance and large resistance?

Answer 26

Takes longer to charge/discharge.

Question 27

What is simple harmonic motion?

Answer 27

An oscillation in which the acceleration of an object is directly proportional to its displacement from the midpoint (and is directed towards the midpoint)

Restoring force is proportional to displacement.

Question 28

Equations for displacement, velocity and acceleration

Answer 28

s = A sin wt

v = Aw cos wt

a = - Aw^2 sin wt
a = -w^2 s

Question 29

What are the two possible oscillation equations?

Answer 29

At maximum displacement at time 0,

s = A cos 2pi f t

At midpoint at time 0,

s = A sin 2pi f t

Question 30

What does it mean to be isochronous?

Answer 30

Pendulums and other oscillators are isochronous meaning that the time period is independent of the amplitude.

Question 31

Energy stored by stretching or compressing a spring:

Answer 31

E = 1/2 k x^2

Question 32

At t = 0

S =
V =
A =

Answer 32

S = A

V = Aw

A = Aw^2

Question 33

Time period of simple harmonic oscillator

Answer 33

T = 2π √(m/k)

Question 34

s’’ =

Answer 34

• k/m x

since F = ma = ms’’

and F = -kx

Question 35

What is the natural frequency of a system?

Answer 35

Frequency it oscillates at with no driving force.

Question 36

Total energy of a freely oscillating mass on a spring

Answer 36

E = KE + PE

E = 1/2 mv^2 + 1/2 kx^2

Question 37

What is resonance?

Answer 37

When the driving frequency = natural frequency the system gains more and more energy from the driving force and thus vibrates with a rapidly increasing amplitude.

Question 38

What does damping do?

Answer 38

Reduces the amplitude of the oscillation over time as the system loses energy to its surroundings.

Question 39

Critical damping

Answer 39

Reduces the amplitude in the shortest possible time.

Question 40

Overdamping

Answer 40

Takes longer to return to equilibrium than a critically damped system.