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A radioactive isotope is being produced at a constant rate dN/

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

_{80}^{197} Hg

decay to

_{79}^{197}

Au through electron capture with a decay constant of

0.257

per day.
(a) What other particle or particles are emitted in the decay?
(b) Assume that the electron is captured from the K shell. Use Moseley's law

v = a (Z - b)

with

a = 4.95 \times

1 0^{7} s^{- 1/2}

and

b = 1

to find the wavelength of the

K_{α}

X-ray emitted following the electron capture.

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life

t_{1/2}

. Show that after a time

t >> t_{1/2}

the number of active nuclei will become constant. Find the value of this constant.

Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.

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Solving time: 5 mins

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life $t_{1/2}$ . Show that after a time $t >> t_{1/2}$ the number of active nuclei will become constant. Find the value of this constant.

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Book:

Concepts of Physics (HC Verma Part II)

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A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life

t_{1/2}

. Show that after a time

t >> t_{1/2}

the number of active nuclei will become constant. Find the value of this constant.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Given:
Half life period of isotope

= t_{1/2}

Disintegration constant,

λ = \frac{0.693}{t _{1/2}}

Rate of Radio active decay (R) is given by,

R = \frac{d N}{d t}

We are to show that after time

t >> t_{1/2}

the number of active nuclei is constant.

(\frac{d N}{d t})_{P_{resent}} = R = (\frac{d N}{d t})_{decay} ∴ R = (\frac{d N}{d t})_{decay}

Rate of radioactive decay,

R = λ N

Here,

λ =

Radioactive decay constant

N = Constant number R = \frac{0.693}{t _{1/2}} \times N \Rightarrow R t_{1/2} = 0.693 N \Rightarrow N = \frac{R t _{1/2}}{0.693}

This value of N should be constant.

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Question Text	A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life $t_{1/2}$ . Show that after a time $t >> t_{1/2}$ the number of active nuclei will become constant. Find the value of this constant.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	57

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life $t_{1/2}$ . Show that after a time $t >> t_{1/2}$ the number of active nuclei will become constant. Find the value of this constant.

Text solutionVerified

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A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life $t_{1/2}$ . Show that after a time $t >> t_{1/2}$ the number of active nuclei will become constant. Find the value of this constant.