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When charcoal is prepared from a living tree, it shows a disin

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

^{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.

Natural water contains a small amount of tritium

(_{1}^{3} H)

. This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the

(_{1}^{3} H)

radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.

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Solving time: 5 mins

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.

Name: Video solution 1: [Solved] When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of 14C per gram per minute. A sample from an ancient piece of charcoal shows 14C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of 14C is 5730 y. - Concepts of Physics
Uploaded: 2022-02-12T21:23:10.000Z
Duration: 2 min
Description: Video solution 1: [Solved] When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of 14C per gram per minute. A sample from an ancient piece of charcoal shows 14C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of 14C is 5730 y. - Concepts of Physics

Views: 5,890 students

Updated on: Feb 12, 2022

Book:

Concepts of Physics (HC Verma Part II)

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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.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Given:

Initial activity of charcoal,

A_{0} = 15.3

disintegrations per gram per minute

Half-life of charcoal,

T_{1/2} = 5730

years

Final activity of charcoal after a few years,

A = 12.3

disintegrations per gram per minute

Disintegration constant,

λ = \frac{0.693}{T _{1/2}} = \frac{0.693}{5370} y^{- 1}

Let the sample take a time of t years for the activity to reach

12.3

disintegrations per gram per minute.

Activity of the sample,

A = A_{0} e^{- λ t}

A = A_{0} e^{- \frac{0.633}{5730} \times t}

\Rightarrow ln \frac{12.3}{15.3} = \frac{- 0.693}{5730} t

\Rightarrow 0.218253 = \frac{0.693}{5730} t

\Rightarrow t = 1804.3 years

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Question Text	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.
Updated On	Feb 12, 2022
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	222
Avg. Video Duration	2 min

Text solutionVerified

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When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of 14C per gram per minute. A sample from an ancient piece of charcoal shows 14C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of 14C is 5730 y.

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