63.
(a) The mass of a
238
U atom is (238 u)(1.661
× 10
−24
g/u) = 3.95
× 10
−22
g, so the number of uranium
atoms in the rock is N
U
= (4.20
× 10
−3
g)/(3.95
× 10
−22
g) = 1.06
× 10
19
. The mass of a
206
Pb
atom is (206 u)(1.661
× 10
−24
g) = 3.42
× 10
−22
g, so the number of lead atoms in the rock is
N
Pb
= (2.135
× 10
−3
g)/(3.42
× 10
−22
g) = 6.24
× 10
18
.
(b) If no lead was lost, there was originally one uranium atom for each lead atom formed by decay,
in addition to the uranium atoms that did not yet decay. Thus, the original number of uranium
atoms was N
U 0
= N
U
+ N
Pb
= 1.06
× 10
19
+ 6.24
× 10
18
= 1.68
× 10
19
.
(c) We use
N
U
= N
U 0
e
−λt
where λ is the disintegration constant for the decay. It is related to the half-life T
1/2
by λ =
(ln 2)/T
1/2
. Thus
t =
−
1
λ
ln
N
U
N
U 0
=
−
T
1/2
ln 2
ln
N
U
N
U 0
=
−
4.47
× 10
9
y
ln 2
ln
1.06
× 10
19
1.68
× 10
19
= 2.97
× 10
9
y .
Document Outline
- Main Menu
- Chapter 1 Measurement
- Chapter 2 Motion Along a Straight Line
- Chapter 3 Vectors
- Chapter 4 Motion in Two and Three Dimensions
- Chapter 5 Force and Motion I
- Chapter 6 Force and Motion II
- Chapter 7 Kinetic Energy and Work
- Chapter 8 Potential Energy and Conservation of Energy
- Chapter 9 Systems of Particles
- Chapter 10 Collisions
- Chapter 11 Rotation
- Chapter 12 Rolling, Torque, and Angular Momentum
- Chapter 13 Equilibrium and Elasticity
- Chapter 14 Gravitation
- Chapter 15 Fluids
- Chapter 16 Oscillations
- Chapter 17 Waves—I
- Chapter 18 Waves—II
- Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
- Chapter 20 The Kinetic Theory of Gases
- Chapter 21 Entropy and the Second Law of Thermodynamics
- Chapter 22 Electric Charge
- Chapter 23 Electric Fields
- Chapter 24 Gauss’ Law
- Chapter 25 Electric Potential
- Chapter 26 Capacitance
- Chapter 27 Current and Resistance
- Chapter 28 Circuits
- Chapter 29 Magnetic Fields
- Chapter 30 Magnetic Fields Due to Currents
- Chapter 31 Induction and Inductance
- Chapter 32 Magnetism of Matter: Maxwell’s Equation
- Chapter 33 Electromagnetic Oscillations and Alternating Current
- Chapter 34 Electromagnetic Waves
- Chapter 35 Images
- Chapter 36 Interference
- Chapter 37 Diffraction
- Chapter 38 Special Theory of Relativity
- Chapter 39 Photons and Matter Waves
- Chapter 40 More About Matter Waves
- Chapter 41 All About Atoms
- Chapter 42 Conduction of Electricity in Solids
- Chapter 43 Nuclear Physics
- 43.1 - 43.10
- 43.1
- 43.2
- 43.3
- 43.4
- 43.5
- 43.6
- 43.7
- 43.8
- 43.9
- 43.10
- 43.11 - 43.20
- 43.11
- 43.12
- 43.13
- 43.14
- 43.15
- 43.16
- 43.17
- 43.18
- 43.19
- 43.20
- 43.21 - 43.30
- 43.21
- 43.22
- 43.23
- 43.24
- 43.25
- 43.26
- 43.27
- 43.28
- 43.29
- 43.30
- 43.31 - 43.40
- 43.31
- 43.32
- 43.33
- 43.34
- 43.35
- 43.36
- 43.37
- 43.38
- 43.39
- 43.40
- 43.41 - 43.50
- 43.41
- 43.42
- 43.43
- 43.44
- 43.45
- 43.46
- 43.47
- 43.48
- 43.49
- 43.50
- 43.51 - 43.60
- 43.51
- 43.52
- 43.53
- 43.54
- 43.55
- 43.56
- 43.57
- 43.58
- 43.59
- 43.60
- 43.61 - 43.70
- 43.61
- 43.62
- 43.63
- 43.64
- 43.65
- 43.66
- 43.67
- 43.68
- 43.69
- 43.70
- 43.71 - 43.80
- 43.71
- 43.72
- 43.73
- 43.74
- 43.75
- 43.76
- 43.77
- 43.78
- 43.79
- 43.80
- 43.81 - 43.88
- 43.81
- 43.82
- 43.83
- 43.84
- 43.85
- 43.86
- 43.87
- 43.88
- 43.1 - 43.10
- Chapter 44 Energy from the Nucleus
- Chapter 45 Quarks, Leptons, and the Big Bang
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