Nuclear Stability

Q. The number of protons, neutrons and electrons in ${}_{71}^{175}Lu$ respectively, are

1. $104,71\text{and}71$
2. $71,71\text{and}104$
3. $175,104\text{and}71$
4. $71,104\text{and}71$

Q. A plot of the number of neutrons ($n$) against the number of protons ($p$) of stable nuclei exhibits upward deviation from linearity for atomic number, $Z>20$. For an unstable nucleus having $n/p$ ratio less than $1$, the possible mode(s) of decay is (are)

1. ${\beta }^{-}-\text{decay}(\beta -\text{emission})$
2. Orbital or K-electron capture
3. Neutron emission
4. ${\beta }^{+}$ - decay (positron emission)

Q. ${}_{17}^{35}Cl$ and ${}_{17}^{37}Cl$ are two isotopes of chlorine. If average atomic mass is $35.5$ then ratio of these two isotopes is:

1. $35:37$
2. $3:1$
3. $1:3$
4. $2:1$

Q.

${13}^{A{l}^{27}}$ is a stable isotope. ${13}^{A{l}^{29}}$ is expected to disintegrate by :

1. $\alpha -$ emission

2. $\beta -$ emission

3. Proton emission

4. Position emission

Q.

Which of the following nuclides is the least stable ?

1. $Z{r}^{91}$

2. $C{O}^{58}$

3. $C^{13}$

4. $N{e}^{20}$

Q.

Match the species im Column I with the bond order in Column II.

	Column I		Column II
A	\(NO\)	\((i)\)	1.5
B	\(CO\)	\((ii)\)	2.0
C	\(O_2^-\)	\((iii)\)	2.5
D	\(O_2\)	\((iv)\)	3.0

Q.

Which of the following nuclides is positron emitter ?

1. $B^{12}$

2. $N^{13}$

3. $H^3$

4. $H^{e^6}$

Q.

1. True
2. False

Q. A plot of the number of neutrons ($n$) against the number of protons ($p$) of stable nuclei exhibits upward deviation from linearity for atomic number, $Z>20$. For an unstable nucleus having $n/p$ ratio less than $1$, the possible mode(s) of decay is (are)

1. ${\beta }^{-}-\text{decay}(\beta -\text{emission})$
2. Orbital or K-electron capture
3. Neutron emission
4. ${\beta }^{+}$ - decay (positron emission)

Q. Cobalt (60) isotope is used in the treatment of:

1. Heart diseases
2. Skin diseases
3. Diabetes
4. Cancer

Q. Which of the following nuclei is unstable ?

1. ${}_5{B}^{10}$
2. ${}_{4}B{e}^{10}$
3. ${}_7{N}^{14}$
4. ${}_8{O}^{16}$

Q. A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having $\frac{N}{P}$ ratio less than 1, the possible mode(s) of decay is(are)

1. ${\beta }^{-}$ - decay ($\beta$ emission)
2. Orbital or K-electron capture
3. Neutron emission
4. ${\beta }^{+}$ - decay (positron emission)

Q. Which of the following atomic mass of uranium is the most radioactive

1. 238
2. 235
3. 226
4. 248

Q. An atomic nucleus having low $n/p$ ratio tries to find stability by :

1. the emission of a positron
2. the emission of an $\alpha$-particle
3. emission of a $\beta$-particle
4. capturing an orbital electron (K-electron capture)

Q. Stable nuclei having number of neutrons less than number of protons are:

1. ${}_2^{3}He$
2. ${}_1^{1}H$
3. ${}_5^{11}B$
4. ${}_6^{11}C$

Q. Which of the following atomic mass of uranium is the most radioactive

1. 238
2. 235
3. 226
4. 248

Q.

Based on magic numbers, which nuclide is the most stable ?

1. $N{i}^{59}$

2. $V^{51}$

3. $C^{12}$

4. $O^{16}$

Q. At radioactive equilibrium, the ratio between the atoms of two radioactive elements A and B was found to be $3.1\times {10}^9$: 1 respectively. If $T_{50}$ of the element A is $2\times {10}^{10}$ yrs, then $T_{50}$ of the element B is :

1. $6.2\times {10}^9$ yr
2. $6.45$ yr
3. $2\times {10}^{10}$ yr
4. $3.1\times {10}^9$ yr

Q.

Which of the following nuclides is the least stable ?

1. $Z{r}^{91}$

2. $C{O}^{58}$

3. $C^{13}$

4. $N{e}^{20}$

Q. Certain isotopes have unstable nucleus because which one of the following?

1. Number of protons outweighs the number of neutrons
2. The number of electrons outweighs the number of protons
3. The number of neutrons outweighs the number of protons
4. The number of protons outweigh the number of electrons
5. The number of neutrons outweighs the number of electrons

Q. Which of the following facts are inferred from the given N vs Z graph?

1. For lighter stable nuclei $\frac{N}{Z}=1$
2. For lighter stable nuclei $\frac{N}{Z}$ > 1
3. For heavier stable nuclei $\frac{N}{Z}=1$
4. For heavier stable nuclei $\frac{N}{Z}$ > 1

Q. Statement I: Neutron to proton ratio less than 1 especially in a heavy nucleus makes it highly unstable.
Statement II: Nucleus where protons are separated by a large distance are dominated by repulsive electrostatic force.

1. Both statements are always true and statement II is the correct reason for statement I
2. Both statements are false
3. Statement I is not always true but II is correct.
4. Statement I is false but II is true.

Q. A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having $\frac{N}{P}$ ratio less than 1, the possible mode(s) of decay is(are)

1. ${\beta }^{-}$ - decay ($\beta$ emission)
2. Orbital or K-electron capture
3. Neutron emission
4. ${\beta }^{+}$ - decay (positron emission)

Q. Calculate the maximum energy of a $\beta -$particle emitted from a ${}^{14}C$ nucleus which does not emit any $\gamma$-radiation. The masses of C-14 and N-14 isotopes are $14.003242$ amu and $14.003074$ amu respectively.

1. $0.1564$ MeV
2. $0.1764$ MeV
3. None of these
4. $0.1464$ MeV

Q. A mixture of${}_{239}$Pu and ${}_{240}$Pu has a specific activity of $6\times {10}^9$ dis/s/g.The half-lives of the isotopes are $2.44\times {10}^4$ year and $6.58\times {10}^3$ year respectively. Calculate the isotopic composition of this sample.

1. ${}_{259}Pu=42\%,$ ${}_{240}Pu=58\%$
2. ${}_{239}Pu=41\%,$ ${}_{240}Pu=59\%$
3. ${}_{259}Pu=40\%,$ ${}_{240}Pu=60\%$
4. ${}_{239}Pu=39\%,$ ${}_{240}Pu=61\%$

Q. Pick the correct option given the following statements:
Statement I Nuclide ${}_{13}^{30}Al$ is less stable than ${}_{20}^{40}Ca$
Statement II Nuclides having odd number of protons and neutrons are generally unstable.

1. Statement I is true; Statement II is true; Statement II is not the correct explanation of Statement I
2. Statement I is true; Statement II is true; Statement II is the correct explanation of Statement I
3. Statement I is true; Statement II is false
4. Statement I is false; Statement II is true

Q. Which can be used for carrying out nuclear reaction

1. Uranium – 238
2. Neptunium – 239
3. Thorium – 232
4. Plutonium – 239

Q. Statement I: Neutron to proton ratio less than 1 especially in a heavy nucleus makes it highly unstable.
Statement II: Nucleus where protons are separated by a large distance are dominated by repulsive electrostatic force.

1. Both statements are always true and statement II is the correct reason for statement I
2. Both statements are false
3. Statement I is not always true but II is correct.
4. Statement I is false but II is true.

Q. Pick the correct option given the following statements:
Statement I Nuclide ${}_{13}^{30}Al$ is less stable than ${}_{20}^{40}Ca$
Statement II Nuclides having odd number of protons and neutrons are generally unstable.

1. Statement I is true; Statement II is true; Statement II is the correct explanation of Statement I
2. Statement I is true; Statement II is true; Statement II is not the correct explanation of Statement I
3. Statement I is true; Statement II is false
4. Statement I is false; Statement II is true

Q. If $M(A;Z),M_p$ and $M_n$ denote the masses of the nucleus ${}_Z^{A}X$, proton and neutron respectively in units of u $(1u=931.5MeV/c^2)$ and BE represents its bonding energy in MeV, then:

1. $M(A,Z)=Z{M}_p+\left(AZ\right)M_{n}BE$
2. $M(A,Z)=Z{M}_p+\left(AZ\right)M_n+BE/c^2$
3. $M(A,Z)=Z{M}_p+(A-Z)M_n-BE/c^2$
4. $M(A,Z)=Z{M}_p+\left(AZ\right)M_n+BE$