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Concepts of Physics

The Nucleus

{}^{238}U decays to {}^{206}Pb with a half-life of 4.47 × 10^9

Concepts of Physics

Class 12

HC Verma Part II

Chapter 1: Heat and Temperature

64 questions

Chapter 2: Kinetic Theory of Gases

100 questions

Chapter 3: Calorimetry

41 questions

Chapter 4: Laws of Thermodynamics

51 questions

Chapter 5: Specific Heat Capacities of Gases

65 questions

Chapter 6: Heat Transfer

82 questions

Chapter 7: Electric Field and Potential

106 questions

Chapter 8: Gauss's Law

46 questions

Chapter 9: Capacitors

94 questions

Chapter 10: Electric Current in Conductors

126 questions

Chapter 11: Thermal and Chemical Effects of Electric Current

46 questions

Chapter 12: Magnetic field

91 questions

Chapter 13: Magnetic field due to a Current

92 questions

Chapter 14: Permanent Magnets

54 questions

Chapter 15: Magnetic Properties of Matter

31 questions

Chapter 16: Electromagnetic Induction

133 questions

Chapter 17: Alternating Current

51 questions

Chapter 18: Electromagnetic Waves

30 questions

Chapter 19: Electric Current through Gases

49 questions

Chapter 20: Photoelectric Effect and Wave Particle Duality

69 questions

Chapter 21: Bohr'a Model and Physics of the Atom

75 questions

Chapter 22: X-rays

59 questions

Chapter 23: Semiconductors and Semiconductor devices

71 questions

Chapter 24: The Nucleus

94 questions

A point source emitting alpha particles is placed at a distance of 1 m from a counter which records any alpha particle falling on its 1 cm

^{2}

window. If the source contains 6.0 × 10

^{16}

active nuclei and the counter records a rate of 50000 counts/second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.

^{238} U

decays to

^{206} P b

with a half-life of

4.47 \times 1 0^{9}

y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of

^{238} U

and 0.600 mg of

^{206} P b .

Assuming that all the lead has come from uranium, find the life of the rock.

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of

^{14}

C per gram per minute. A sample from an ancient piece of charcoal shows

^{14}

C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of

^{14}

C is 5730 y.

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Question

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Solving time: 5 mins

$^{238} U$ decays to $^{206} P b$ with a half-life of $4.47 \times 1 0^{9}$ y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of $^{238} U$ and 0.600 mg of $^{206} P b .$ Assuming that all the lead has come from uranium, find the life of the rock.

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Book:

Concepts of Physics (HC Verma Part II)

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^{238} U

decays to

^{206} P b

with a half-life of

4.47 \times 1 0^{9}

y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of

^{238} U

and 0.600 mg of

^{206} P b .

Assuming that all the lead has come from uranium, find the life of the rock.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Given:

Half-life of

^{238} U, t_{1/2} = 4.47 \times 1 0^{9}

years

Total Number of atoms present in the rock initially,

N_{0} = (\frac{6.023 \times 1 0 ^{23} \times 2}{238} + \frac{6.023 \times 1 0 ^{23} \times 0.6}{206})

= (\frac{12.046}{238} + \frac{3.62}{206}) \times 1 0^{20}

= (0.0505 + 0.0175) \times 1 0^{20}

= 0.0680 \times 1 0^{20}

Now,

N = N_{0} e^{- λ t}

Here,

λ =

Disintegration constant

t =

Life of the rock

\Rightarrow N = N_{0} e^{\frac{- 0.603}{1/2}} \times t

\Rightarrow 0.0505 = 0.0680 e^{\frac{- 0.693}{4.47 \times 1 0 ^{9}} \times t}

\Rightarrow ln (\frac{0.0505}{0.0680}) = \frac{- 06931}{4.47 \times 1 0 ^{9}} \times t

\Rightarrow t = 1.92 \times 1 0^{9} years

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Question Text	$^{238} U$ decays to $^{206} P b$ with a half-life of $4.47 \times 1 0^{9}$ y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of $^{238} U$ and 0.600 mg of $^{206} P b .$ Assuming that all the lead has come from uranium, find the life of the rock.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	75

Text solutionVerified

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