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Physics Part-II

Nuclei

For the ^+ (positron) emission from a nucleus, there is anothe

Physics Part-II

Class 12

NCERT

Chapter 1: Ray Optics and Optical Instruments

41 questions

Chapter 2: Wave Optics

30 questions

Chapter 3: Dual Nature of Radiation and Matter

44 questions

Chapter 4: Atoms

23 questions

Chapter 5: Nuclei

38 questions

From the relation R =

R_{0} A^{\frac{1}{3}}

, where

R_{0}

is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

For the

β^{+}

(positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K shell, is captured by the nucleus and a neutrino is emitted).

e^{+} +_{Z}^{A} X \to_{Z - 1}^{A} Y + v

Show that if

β^{+}

emission is energetically allowed, electron capture is necessarily allowed but not vice versa.

In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are

_{12}^{24} M g

(23.98504u),

_{12}^{25} M g

(24.98584u) and

_{12}^{26} M g

(25.98259u). The natural abundance of

_{12}^{24} M g

is 78.99% by mass. Calculate the abundances of other two isotopes.

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Chapter 6: Semiconductor Electronics: Materials, Devices and Simple Circuits

25 questions

Question

Medium

Solving time: 4 mins

For the $β^{+}$ (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K shell, is captured by the nucleus and a neutrino is emitted).
$e^{+} +_{Z}^{A} X \to_{Z - 1}^{A} Y + v$
Show that if $β^{+}$ emission is energetically allowed, electron capture is necessarily allowed but not vice versa.

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Physics Part-II (NCERT)

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William Discussed

For the

β^{+}

e^{+} +_{Z}^{A} X \to_{Z - 1}^{A} Y + v

Show that if

β^{+}

emission is energetically allowed, electron capture is necessarily allowed but not vice versa.

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Consider the competing processes:

_{Z}^{A} W \to_{Z - 1}^{A} Y + e^{+} + v_{e} + Q_{1}

(positron cature)

e^{-} +_{Z}^{A} W \to_{Z - 1}^{A} Y + v_{e} + Q_{2}

(electron capture)

Q_{1} = [m_{N} (_{Z}^{A} X) - m_{N} (_{Z - 1}^{A} Y) - m_{e}] c^{2}

= [m_{N} (_{Z}^{A} X) - Z m_{e} - m (_{Z - 1}^{A} Y) - (Z - 1) m_{e} - m_{e}] c^{2}

= [m_{N} (_{Z}^{A} X) - m_{N} (A_{Z - 1} Y) - 2 m_{e}] c^{2}

Q_{2} = [m_{N} (_{Z}^{A} X) + m_{e} - m_{N} (_{Z - 1}^{A} Y)] c^{2} = [m (_{Z}^{A} X) - m (_{Z - 1}^{A} Y)] c^{2}

This means

Q_{1} > 0

implies

Q_{2} > 0

, but

Q_{2} > 0

does not necessarily mean

Q_{1} > 0

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Practice more questions from Physics Part-II (NCERT)

From the relation R =

R_{0} A^{\frac{1}{3}}

, where

R_{0}

is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

For the

β^{+}

e^{+} +_{Z}^{A} X \to_{Z - 1}^{A} Y + v

Show that if

β^{+}

emission is energetically allowed, electron capture is necessarily allowed but not vice versa.

In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are

_{12}^{24} M g

(23.98504u),

_{12}^{25} M g

(24.98584u) and

_{12}^{26} M g

(25.98259u). The natural abundance of

_{12}^{24} M g

is 78.99% by mass. Calculate the abundances of other two isotopes.

View all

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Question Text	For the $β^{+}$ (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K shell, is captured by the nucleus and a neutrino is emitted). $e^{+} +_{Z}^{A} X \to_{Z - 1}^{A} Y + v$ Show that if $β^{+}$ emission is energetically allowed, electron capture is necessarily allowed but not vice versa.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	68

Text solutionVerified

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