Q. No.Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half-life of 1 yr. After 1yr,
1. all the containers will have 5000 atoms of the material
2. all the containers will contain the same number of atoms of the material but that number will only be approximately 5000
3. the containers will in general have different numbers of the atoms of the material but their average will be close to 5000
4. none of the containers can have more than 5000 atoms
| 1. | \(M = m_{\text{proton}}+ m_{\text{electron}}.\) |
| 2. | \(M = m_{\text{proton}}+ m_{\text{electron}}-\frac{B}{c^2}\left(B= 13.6~\text{eV}\right)\). |
| 3. | \(M\) is not related to the mass of the hydrogen atom. |
| 4. | \(M = m_{\text{proton}}+ m_{\text{electron}}-\frac{|V|}{c^2}(|V|=\) magnitude of the potential energy of electron in the \(\text H\text-\)atom). |
| 1. | do not change for any type of radioactivity |
| 2. | change for \(\alpha\) and \(\beta\text-\)radioactivity but not for \(\gamma\text-\)radioactivity |
| 3. | change for \(\alpha\text-\)radioactivity but not for others |
| 4. | change for \(\beta\text-\)radioactivity but not for others |
\(M_x\) and \(M_y\) denote the atomic masses of the parent and the daughter nuclei respectively in radioactive decay. The \(Q\text -\)value for a \(\beta^{-}\) decay is \(Q_1\) and that for a \(\beta^{+}\) decay is \(Q_2.\) If \(m_e\) denotes the mass of an electron, then which of the following statements is correct?
| 1. | \(\small[Q_1=\left(M_x-M_y\right) c^2 \text { and } Q_2=\left[M_x-M_y-2 m_e\right] c^2 \) |
| 2. | \( \small[Q_1=\left(M_x-M_y\right) c^2 \text { and } Q_2=\left(M_x-M_y\right) c^2 \) |
| 3. | \(\small[Q_1=\left(M_x-M_y-2 m_e\right)c^2 \text { and } Q_2=\left(M_x-M_y+2 m_e\right) c^2 \) |
| 4. | \(\small[Q_1=\left(M_x-M_y+2 m_e\right) c^2 \text { and } Q_2=\left(M_x-M_y+2 m_e\right) c^4 \) |
| 1. | triton energy is less than that of a \(\mathrm{He}^{3}\) nucleus. |
| 2. | the electron created in the beta decay process cannot remain in the nucleus. |
| 3. | both the neutrons in Triton have to decay simultaneously resulting in a nucleus with \(3\) protons, which is not a \(\mathrm{He}^{3}.\) nucleus. |
| 4. | free neutrons decay due to external perturbations which is absent in the Triton nucleus. |
Heavy stable nuclei haveVc2 more neutrons than protons. This is because of the fact that
1. neutrons are heavier than protons
2. electrostatic force between protons is repulsive
3. neutrons decay into protons through beta decay
4. nuclear forces between neutrons are weaker than that between protons
In a nuclear reactor, moderators slow down the neutrons which come out in a fission process. The moderator used have light nuclei. The heavy nuclei will not serve the purpose, because:
| 1. | they will break up |
| 2. | elastic collision of neutrons with heavy nuclei will not slow them down |
| 3. | the net weight of the reactor would be unbearably high |
| 4. | substances with heavy nuclei do not occur in the liquid or gaseous state at room temperature |
| (a) | nuclear forces have short-range. |
| (b) | nuclei are positively charged. |
| (c) | the original nuclei must be completely ionized before fusion can take place. |
| (d) | the original nuclei must first break up before combining with each other. |
Choose the correct option:
| 1. | (a) and (c) | 2. | (a) and (d) |
| 3. | (b) and (d) | 4. | (a) and (b) |
Samples of two radioactive nuclides A and B are taken. and 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?
(a) Initial rate of decay of A is twice the initial rate of decay of B and =
(b) Initial rate of decay of A is twice the initial rate of decay of B and >
(c) Initial rate of decay of B is twice the initial rate of decay of A and >
(d) Initial rate of decay of B is same as the rate of decay of A at t = 2 h and <
1. (a, b)
2. (a, c)
3. (b, d)
4. (c, d)
The variation of the decay rate of two radioactive samples A and B with time is shown in the figure.
Which of the following statements are true?
| a. | Decay constant of A is greater than that of B, hence A always decays faster than B |
| b. | Decay constant of B is greater than that of A but its decay rate is always smaller than that of A |
| c. | Decay constant of A is greater than that of B but it does not always decay faster than B |
| d. | Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant |
1. (a, b)
2. (a, c)
3. (b, d)
4. (c, d)
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