Tag: nuclear physics

Questions Related to nuclear physics

Initial number of nuclei of a radioactive substance is $5 \times 10 ^ { 16 }$ and half-life is $10$ yrs. Find the number of nuclei decayed in $5$ yrs.

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $2 \times 10 ^ { 16 }$

  2. $1.5 \times 10 ^ { 16 }$

  3. $3.5 \times 10 ^ { 16 }$

  4. $2.5 \times 10 ^ { 16 }$

Show answer
Correct Option: B
Explanation:

$Remaining$ nuclei after $5$ years will be $N=5\times 10^{16} \times (\dfrac{1}{2})^{5/10}=\dfrac{5\times 10^{16}}{\sqrt[2]{2}}=\dfrac{5\times 10^{16}}{1.414}=3.54\times 10^{16}$


So the decayed nuclei will be $(5-3.54)\times 10^{16}=1.46\times 10^{16}$
nearly $1.5\times 10^{16}$

A mixture consists of two radioactive materials ${ A } _{ 1 }$ and ${ A } _{ 2 }$ with half lives of 20 s and 10 s respectively. Initially the mixture has $40 g$ of ${ A } _{ 1 }$ and $160 g$ of ${ A } _{ 2 }$. The active amount of the two in the mixture will become equal after :

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $20s$

  2. $40s$

  3. $60s$

  4. $80s$

Show answer
Correct Option: B

Samples of two radioactive nuclides $A$ and $B$ are taken. $\lambda _ { A }$ and $\lambda _ { B }$ are the disintegration constants of $A$ and $B$ respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time ? 

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. Initial rate of decay of $A$ is twice the initial rate of decay of $B$ and $\lambda _ { A } = \lambda _ { B }$

  2. Initial rate of decay of $A$ is twice the initial rate of decay of $B$ and $\lambda _ { A } > \lambda _ { B }$

  3. Initial rate of decay of $B$ is twice the initial rate of decay of $A$ and $\lambda _ { A } > \lambda _ { B }$

  4. Initial rate of decay of $B$ is same as the rate of decay of $A$ at t = 2h and $\lambda _ { B } < \lambda _ { A }$

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} N={ N _{ 0 } }{ e^{ -\lambda t } } \ \therefore if\, initial\, rate\, is\, same\, \, and\, { \lambda _{ A } }={ \lambda _{ B } } \end{array}$

Hence,
option $(A)$ is correct answer.

The radius of spherical nucleus as measured by electron scattering is 36. fm. what is the likely mass number of the nucleus?

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. 27

  2. 40

  3. 56

  4. 120

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Correct Option: A

A radioactive element $ _ { 90 } \mathrm { X } ^ { 238 }$ decays into $\mathrm { 83 } \mathrm { Y } ^ { 222 }$,then the number of $\beta$ -particles emitted are

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $1$

  2. $2$

  3. $4$

  4. $6$

Show answer
Correct Option: C

A bone containing 200 g carbon-14 has a $\beta $ decay rate of 375 deacy/min. Calculate the time that has elapsed since the death of the living one. Given the rate of decay for the living organism is equal to 15 decay per min per gram of carbon and half - life of carbon -14 is 5730 years,

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. 27190 years

  2. 1190 years

  3. 17190 years

  4. None of these

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Correct Option: A

A nucleus X undergoes following transformation
$x \stackrel { a } { \longrightarrow } Y$
$Y \longrightarrow Z$

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $x$ and $Y$ are isotopes

  2. $x$ and $Z$ are isobars

  3. $x$ and $Y$ are isobars

  4. $x$ and $Z$ are isotopes

Show answer
Correct Option: A

From the following the wrong statement is:

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. Half-life of a free neutron is $10.3$ minutes

  2. The stability of a nucleus is only determined by the number of neutrons present in it.

  3. Both fast and slow neutrons are capable of penetrating the nucleus

  4. A free neutron decays into a proton, an electron and positron

Show answer
Correct Option: D
Explanation:

A free neutron will decay with a half life of about $10.3$ minutes but it is stable if combined into a nucleus. The stability of a nucleus is determined by number of neutrons as well as protons, Only fast moving neutrons are capable of penetrating the nucleus.A few neutron decays into a proton, an electron and anti-neutrino, and other options are known facts.

When $ _{3}Li^{7}$ nuclei are bombarded by protons, and the resultant nuclei are $ _{4}Be^{8}$ , the emitted particles will be.   

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. alpha particles

  2. beta particles

  3. gamma photons

  4. neutrons

Show answer
Correct Option: C
Explanation:

$ _{3}Li^{7} + ^{1} _{1}P \Rightarrow  _{4}Be^{8} + _{0}^{0}\gamma (energy)$
As, the emitted particles is only energy and gamma photons radiation is nothing but energy so, option  C is correct.

$ {27}^{57}\textrm{Co}$ will emit __________ radiation

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $\beta^{-}$

  2. $ \beta^{+}$

  3. $\alpha$

  4. electron capture

Show answer
Correct Option: D
Explanation:

Electron capture :   $^{57} _{27}$  $ + $ $ ^0 _{-1}e$ $\rightarrow$  $^{57} _{26}Fe$