Q. No.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. \(1:1\)
1. \(1:3\)
2. \(3:1\)
3. \((3)^{1/3}:1\)
4. \(1:1\)
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. |
A nucleus \({ }_{{n}}^{{m}} \mathrm{X}\) emits one \(\alpha\text -\text{particle}\) 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. | \(^{m-6}_{n-4} \mathrm{Z} \) |
An element \(\mathrm{X}\) decays, first by positron emission, and then two \(\alpha\text-\)particles are emitted in successive radioactive decay. If the product nuclei have a mass number \(229\) and atomic number \(89\), the mass number and the atomic number of element \(\mathrm{X}\) are:
1. \(237,~93\)
2. \(237,~94\)
3. \(221,~84\)
4. \(237,~92\)
| 1. | \(\dfrac{(Z - 13)}{\left(A - Z - 23\right)}\) | 2. | \(\dfrac{\left(Z - 18\right)}{\left(A - 36\right)}\) |
| 3. | \(\dfrac{\left(Z - 13\right)}{\left(A - 36\right)}\) | 4. | \(\dfrac{\left(Z - 13\right)}{\left(A - Z - 13\right)}\) |
\(2~{ }_{6}^{12} \mathrm{C}\rightarrow{ }_{10}^{20} \mathrm{Ne}+{ }_2^4 \mathrm{He}\)
The following data are given:
\(m({ }_{6}^{12} \mathrm{C})=12.000000~\text{amu}\)
\(m({ }_{10}^{20} \mathrm{Ne})=19.992439~\text{amu}\)
\(m({ }_{2}^{4} \mathrm{He})=4.002603~\text{amu}\)
1. \(3.16~\text{MeV}\)
2. \(5.25~\text{MeV}\)
3. \(3.91~\text{MeV}\)
4. \(4.65~\text{MeV}\)
(Energy released per fission of \(\mathrm{U}^{235}=200\) MeV watts, \(1~\text{eV}= 1.6\times 10^{-19}~\text{J})\)
| 1. | \(1.5\times 10^{17}\) | 2. | \(3\times 10^{19}\) |
| 3. | \(1.5\times 10^{25}\) | 4. | \(3\times 10^{25}\) |
The Binding energy per nucleon of \(^{7}_{3}\mathrm{Li}\) and \(^{4}_{2}\mathrm{He}\) nucleon are \(5.60~\text{MeV}\) and \(7.06~\text{MeV}\), respectively. In the nuclear reaction \(^{7}_{3}\mathrm{Li} + ^{1}_{1}\mathrm{H} \rightarrow ^{4}_{2}\mathrm{He} + ^{4}_{2}\mathrm{He} +Q\), the value of energy \(Q\) released is:
1. \(19.6~\text{MeV}\)
2. \(-2.4~\text{MeV}\)
3. \(8.4~\text{MeV}\)
4. \(17.3~\text{MeV}\)
| 1. | It may emit \(\alpha\text-\)particle. |
| 2. | It may emit \(\beta^{+}\) particle. |
| 3. | It may go for \(K\) capture. |
| 4. | All of the above are possible. |
\({}_{1}^{2}\mathrm{H}+ {}_{1}^{2}\mathrm{H}\rightarrow {}_{2}^{4}\mathrm{He}+Q\)
Given: \(M\left({}_{1}^{2}\mathrm{H}\right)= 2.01471~\text{amu}, M\left({}_{2}^{4}\mathrm{He}\right)= 4.00388~\text{amu}\)
1. \(3.79\) MeV
2. \(13.79\) MeV
3. \(0.79\) MeV
4. \(23.79\) MeV
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