MCQ 1

The binding energy for nucleus A is $7.7 \, \mathrm{MeV}$ and for nucleus B is $7.8 \, \mathrm{MeV}$. Which nucleus has the larger mass?

Options
1. Nucleus A
2. Nucleus B ✅
3. Less than nucleus A
4. None

Explanation:

The binding energy is related to the mass defect by:

$$\mathrm{B.E} = \Delta m c^2$$

Nucleus B, having a larger binding energy, will have a larger mass.

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MCQ 2

How many neutrons are there in the nuclide $\mathbf{Zn}^{66}$?

Options
1. 22
2. 30
3. 36 ✅
4. 66

Explanation:

The number of neutrons is given by:

$$N = A - Z = 66 - 30 = 36$$

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MCQ 3

Mass equivalent of $931 \, \mathrm{MeV}$ energy is:

Options
1. $6.02 \times 10^{-23} \, \mathrm{kg}$
2. $1.766 \times 10^{-27} \, \mathrm{kg}$ ✅
3. $2.67 \times 10^{-27} \, \mathrm{kg}$
4. $6.02 \times 10^{-27} \, \mathrm{kg}$

Explanation:

Using $E = mc^2$, we solve:

$$931 \times 10^6 \cdot 1.6 \times 10^{-19} = m \cdot (3 \times 10^8)^2$$ $$m = \frac{931 \times 10^6 \cdot 1.6 \times 10^{-19}}{(3 \times 10^8)^2} = 1.766 \times 10^{-27} \, \mathrm{kg}$$

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MCQ 4

The energy equivalent of $1 \, \mathrm{kg}$ of matter is about:

Options
1. $10^{-15} \, \mathrm{J}$
2. $1 \, \mathrm{J}$
3. $10^{-12} \, \mathrm{J}$
4. $10^{17} \, \mathrm{J}$ ✅

Explanation:

Using $E = mc^2$:

$$E = (1)(3 \times 10^8)^2 = 9 \times 10^{16} \, \mathrm{J} \approx 10^{17} \, \mathrm{J}$$

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MCQ 5

The radioactive nuclide $\mathrm{Ra}^{228}_{88}$ decays by emitting three alpha particles and one beta particle. The resulting nuclide is:

Options
1. $\mathrm{X}^{220}_{84}$
2. $\mathrm{X}^{222}_{86}$
3. $\mathrm{X}^{216}_{83}$ ✅
4. $\mathrm{X}^{215}_{88}$

Explanation:

The decay sequence:

$$\mathrm{Ra}^{228}_{88} \xrightarrow{3\alpha} \mathrm{Y}^{216}_{82} \xrightarrow{\beta} \mathrm{X}^{216}_{83}$$

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MCQ 6

A radioactive substance has a half-life of four months. How long will it take for three-fourths of the substance to decay?

Options
1. 6 months
2. 8 months ✅
3. 12 months
4. 16 months

Explanation:

Fraction remaining:

$$\text{Remaining} = 1 - \left(\frac{1}{2}\right)^2 = \frac{3}{4}$$

Two half-lives correspond to $4 \, \mathrm{months} \times 2 = 8 \, \mathrm{months}$.

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MCQ 7

Gamma radiations are emitted due to:

Options
1. De-excitation of atom
2. De-excitation of nucleus ✅
3. Excitation of atom
4. Excitation of nucleus

Explanation:

Gamma rays result from the de-excitation of nuclei, releasing excess energy.

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MCQ 8

Unit of decay constant $\lambda$:

Options
1. ms
2. $\mathrm{m}^{-1}$
3. m
4. $\mathrm{s}^{-1}$ ✅

Explanation:

The decay constant is:

$$\lambda = \frac{\Delta N / N}{\Delta t}$$

Units are $\mathrm{s}^{-1}$.

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MCQ 9

Which of the following basic forces provides attraction between two neutrons?

Options
1. Electrostatic and nuclear
2. Electrostatic and gravitational
3. Gravitational and strong nuclear ✅
4. Only nuclear force

Explanation:

Gravitational and strong nuclear forces are both attractive.

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MCQ 10

The charge on a bottom quark is:

Options
1. $\frac{2}{3} e$
2. $\frac{-2}{3} e$
3. $\frac{+1}{3} e$
4. $\frac{-1}{3} e$ ✅

Explanation:

A bottom quark has a charge of $\frac{-1}{3} e$.