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If \(M(A,~Z)\), \(M_p\)${}_{}$, and \(M_n\) denote the masses of the nucleus \(^{A}_{Z}X,\) proton, and neutron respectively in units of \(u\) (\(1~u=931.5~\text{MeV/c}^2\)) and represent its binding energy \((BE)\) in \(\text{MeV}\). Then:

1. | \(M(A, Z) = ZM_p + (A-Z)M_n- \frac{BE}{c^2}\) |

2. | \(M(A, Z) = ZM_p + (A-Z)M_n+ BE\) |

3. | \(M(A, Z) = ZM_p + (A-Z)M_n- BE\) |

4. | \(M(A, Z) = ZM_p + (A-Z)M_n+ \frac{BE}{c^2}\) |

Subtopic: Mass-Energy Equivalent |

71%

From NCERT

AIPMT - 2008

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Two nuclei have their mass numbers in the ratio of \(1:3.\) The ratio of their nuclear densities would be:

1. \(1:3\)

2. \(3:1\)

3. \((3)^{1/3}:1\)

4. \(1:1\)

Subtopic: Nucleus |

78%

From NCERT

AIPMT - 2008

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In the radioactive decay process, the negatively charged emitted β-particles are:

1. | the electrons present inside the nucleus |

2. | the electrons produced as a result of the decay of neutrons inside the nucleus |

3. | the electrons produced as a result of collisions between atoms |

4. | the electrons orbiting around the nucleus |

Subtopic: Types of Decay |

79%

From NCERT

AIPMT - 2007

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A nucleus ${}_{Z}{X}^{A}$ has a mass represented by \(M(A, Z).\) If *\(M_P\)* and *\(M_n\)* denote the mass of proton and neutron respectively and BE the binding energy, then:

1. $BE=\left[M\right(A,Z)-Z{M}_{p}-(A-Z\left){M}_{n}\right]{c}^{2}$

2. $BE=[Z{M}_{p}+(A-Z){M}_{n}-M(A,$ $Z\left)\right]{c}^{2}$

3. $BE=[Z{M}_{p}+A{M}_{n}-M-(A,$ $Z\left)\right]{c}^{2}$

4. $BE=M(A,$ $Z)-Z{M}_{p}-(A-Z){M}_{n}$

Subtopic: Nuclear Binding Energy |

82%

From NCERT

AIPMT - 2007

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The binding energy of deuteron is \(2.2~\text{MeV}\) and that of \(_2\mathrm{He}^{4}\) is \(28~\text{MeV}\). If two deuterons are fused to form one \(_{2}\mathrm{He}^{4}\), ${\mathrm{}}^{}$then the energy released is:

1. \(25.8~\text{MeV}\)

2. \(23.6~\text{MeV}\)

3. \(19.2~\text{MeV}\)

4. \(30.2~\text{MeV}\)

Subtopic: Nuclear Binding Energy |

73%

From NCERT

AIPMT - 2006

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The decay constants of two radioactive materials X_{1} and X_{2} are \(5\lambda\) and \(\lambda\) respectively. Initially, they have the same number of nuclei. The ratio of the number of nuclei of X_{1} to that of X_{2 } will be \(1/e\) after a time:

1. \(\lambda\)

2. \(\frac{1}{2\lambda }\)

3. \(\frac{1}{4\lambda }\)

4. \(\frac{e}{\lambda }\)

Subtopic: Types of Decay |

79%

From NCERT

AIPMT - 2008

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The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

1. Isobar of a parent.

2. Isomer of a parent.

3. Isotone of a parent.

4. Isotope of a parent.

Subtopic: Types of Decay |

65%

From NCERT

AIPMT - 2009

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In the nuclear decay given below:

\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow { }_{\mathrm{Z}+1}^{\mathrm{A}} \mathrm{Y}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\)

the particles emitted in the sequence are:\({ }_{\mathrm{Z}}^{\mathrm{A}} \mathrm{X} \rightarrow { }_{\mathrm{Z}+1}^{\mathrm{A}} \mathrm{Y}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\rightarrow { }_{\mathrm{Z-1}}^{\mathrm{A-4}} \mathrm{B}\)

1. \(\beta, \alpha, \gamma\)

2. \( \gamma, \beta, \alpha\)

3. \(\beta, \gamma,\alpha\)

4. \(\alpha,\beta, \gamma\)

Subtopic: Types of Decay |

89%

From NCERT

AIPMT - 2009

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The mass of a ${}_{3}{}^{7}\mathrm{Li}$ nucleus is \(0.042~\text{u}\) less than the sum of the masses of all its nucleons. The binding energy per nucleon of the ${}_{3}{}^{7}\mathrm{Li}$ nucleus is near:

1. \(4.6~\text{MeV}\)

2. \(5.6~\text{MeV}\)

3. \(3.9~\text{MeV}\)

4. \(23~\text{MeV}\)

Subtopic: Nuclear Binding Energy |

72%

From NCERT

AIPMT - 2010

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A nucleus \({ }_{{n}}^{{m}} \mathrm{X}\) emits one $\mathrm{}$\(\alpha\text -\text{particle}\) and two \(\beta\text- \text{particle}\) The resulting nucleus is:

1. \(^{m-}{}_n^6 \mathrm{Z} \)

2. \(^{m-}{}_{n}^{4} \mathrm{X} \)

3. \(^{m-4}_{n-2} \mathrm{Y}\)

4. \(^{m-6}_{n-4} \mathrm{Z} \)

Subtopic: Types of Decay |

81%

From NCERT

AIPMT - 2011

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