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Concepts of Physics

The Nucleus

Natural water contains a small amount of tritium ({ }_{1}^{3}

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

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.

The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing

^{128}

I varies with time as follows.

(a) Plot In

l e f t (R_{0} / R i g h t)

against t.
(b) From the slope of the best straight line through the points, find the decay constant

l amb d a .

ma t h r m t_{1/2}

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Question

Medium

Solving time: 5 mins

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.

Uploaded: 2022-10-18T10:31:34.000Z
Duration: 3 min

Views: 6,022 students

Updated on: Oct 6, 2023

Book:

Concepts of Physics (HC Verma Part II)

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Elijah Discussed

Natural water contains a small amount of tritium

(_{1}^{3} H)

(_{1}^{3} H)

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

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Given:
Half-life time of tritium,

T_{1/2} = 12.5

years
Disintegration constant,

λ = \frac{0.693}{12.5}

per year

Let

A_{0}

be the activity, when the bottle was manufactured.

Activity after 8 years

(A)

is given by

A = A_{0} e^{\frac{- 0.693}{12.5} \times 8}

Let us consider that the mountaineering had taken place

t

years ago. Then, activity of the bottle (A') on the mountain is given by

A^{'} = A_{0} e^{- λ t}

Here,

A^{'} =

(Activity of the bottle manufactured 8 years ago)

\times 1.5%

A^{'} = A_{0} e^{\frac{- 0.603}{12.5} \times 8} \times 0.015

Comparing (1) and (2)

\frac{- 0.693}{12.5} t = \frac{- 0.6931 \times 8}{12.5} + ln [0.015]

\Rightarrow \frac{- 0.693}{12.5} t = \frac{- 0.693}{12.5} \times 8 - 4.1997

\Rightarrow 0.639 t = 58.040

\Rightarrow t = 83.75 years

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Question Text	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.
Updated On	Oct 6, 2023
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 2
Upvotes	227
Avg. Video Duration	2 min

Text solutionVerified

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