- 1(current)
Q. No.The ratio of the mass densities of the nuclei \({ }^{40} \mathrm{Ca}\) and \({ }^{16} \mathrm{O}\) is close to:
| 1. | \(0.1\) | 2. | \(2\) |
| 3. | \(5\) | 4. | \(1\) |
The radius \(R\) of a nucleus of mass number \(A\) can be estimated by the formula \({R}=\left(1.3 \times 10^{-15}\right) A^{1 / 3} ~\text{m}\) , It follows that the mass density of a nucleus is of the order of: \(\left(M_{\text {propt. }}=M_{\text {neut. }}=1.67 \times 10^{-27} ~\text{kg}\right)\)
1. \( 10^{10}~ \text{kg}\text{m}^{-3} \)
2. \( 10^{24} ~\text{kg} \text{m}^{-3} \)
3. \( 10^{17} ~\text{kg} \text{m}^{-3} \)
4. \( 10^{3} ~\text{kg} \text{m}^{-3} \)
The four graphs show different possible relationships between \(\text{ln}\left(\dfrac{{R}}{{R}_0}\right)\) and \(\text{ln}(A).\)
(where \(R\) is the radius of a nucleus and \(A \) is the mass number of the nucleus)
Which of these graphs (1, 2, 3, or 4) correctly represents the relationship between these nuclear parameters?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
1. \(4: 3 \)
2. \(\left(\frac{3}{4}\right)^{\frac{1}{3}} \)
3. \(1: 1 \)
4. \(\left(\frac{4}{3}\right)^{\frac{1}{3}}\)
| A. | Volume of the nucleus is directly proportional to the mass number. |
| B. | Volume of the nucleus is independent of mass number. |
| C. | Density of the nucleus is directly proportional to the mass number. |
| D. | Density of the nucleus is directly proportional to the cube root of the mass number. |
| E. | Density of the nucleus is independent of the mass number. |
| 1. | (A) and (D) only. |
| 2. | (A) and (E) only. |
| 3. | (B) and (E) only. |
| 4. | (A) and (C) only. |
1. \(1:10\)
2. \(10:1\)
3. \(1:1\)
4. \(1:2\)
| 1. | \(\left ( \dfrac{2}{3} \right )^{1/2}\) | 2. | \(\left ( \dfrac{2}{3} \right )^{1/3}\) |
| 3. | \(\left ( \dfrac{4}{9} \right )^{1/3}\) | 4. | \(\left ( \dfrac{9}{4} \right )^{1/2}\) |
1. \(2\)
2. \(2^{1/3}\)
3. \(2^{2/3}\)
4. \(2^{(-1/3)}\)
- 1(current)
Q. No.
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