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. \(1\)
Subtopic:  Nucleus |
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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. \( 10^{3} ~\text{kg} \text{m}^{-3} \)

Subtopic:  Nucleus |
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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.
Subtopic:  Nucleus |
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Mass numbers of two nuclei are in the ratio of 4:3. Their nuclear densities will be in the ratio of
1. \(4: 3 \) 
2. \(\left(\frac{3}{4}\right)^{\frac{1}{3}} \)
3. \(1: 1 \)
4. \(\left(\frac{4}{3}\right)^{\frac{1}{3}}\)
Subtopic:  Nucleus |
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Read the following statements:
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.
Choose the correct option from the following options.
1. (A) and (D) only.
2. (A) and (E) only.
3. (B) and (E) only.
4. (A) and (C) only.
Subtopic:  Nucleus |
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Let nuclear densities of \({}_{2}^{4}{\mathrm{He}}\) and \({}_{20}^{40}{\mathrm{Ca}}\) be \(\rho_1\) and \(\rho_2\) respectively. Then \({{\rho_{1}}\over{\rho_{2}}}\) is equal to:
1. \(1:10\)
2. \(10:1\)
3. \(1:1\)
4. \(1:2\)
Subtopic:  Nucleus |
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A stationary nucleus breaks into two daughter nuclei, which move with velocities in the ratio \(3:2.\) What is the ratio of their nuclear radii?
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. \(\left ( \dfrac{9}{4} \right )^{1/2}\)
Subtopic:  Nucleus |
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If a nucleus is divided in the ratio of \(1:2^{1/3},\) what is the ratio of the velocities of the resulting parts?
1. \(2\) 2. \(2^{1/3}\)
3. \(2^{2/3}\) 4. \(2^{(-1/3)}\)
Subtopic:  Nucleus |
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A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \(2:1\). After disintegration they will move:
1. in opposite directions with the same speed
2. in opposite directions with the speed in the ratio of \(1:2\) respectively.
3. in opposite directions with the speed in the ratio of \(2:1\) respectively.
4. in the same direction with same speed.

 
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