Neutron scattering experiments have shown that the radius of the nucleus of an atom is directly proporitonal to the cube root of the number of nucleons in the nucleus. From `_(3)^(7)Li` to `_(76)^(189)Os` the radius is:

Options

A. Halved
B. the same
C. Doubled
D. Tripled

Explanation

To solve the problem, we need to determine the relationship between the radius of the nucleus and the number of nucleons (protons and neutrons) in the nucleus. The relationship is given as follows:

1. **Understanding Nucleons**: Nucleons are the particles found in the nucleus of an atom, which include both protons and neutrons.

2. **Formula for Nuclear Radius**: The radius \( R \) of the nucleus is directly proportional to the cube root of the number of nucleons \( A \) (where \( A \) is the total number of protons and neutrons). This can be expressed mathematically as:
\[ R \propto A^{1/3} \]
or
\[ R = R_0 A^{1/3} \]
where \( R_0 \) is a constant.

3. **Identifying Nucleon Counts**:
- For Lithium-7 (\( _{3}^{7}Li \)), the number of nucleons \( A \) is 7 (3 protons + 4 neutrons).
- For Osmium-189 (\( _{76}^{189}Os \)), the number of nucleons \( A \) is 189 (76 protons + 113 neutrons).

4. **Calculating the Ratio of Radii**: We need to find the ratio of the radius of Osmium to the radius of Lithium:
\[ \frac{R_{Os}}{R_{Li}} = \frac{R_0 (189)^{1/3}}{R_0 (7)^{1/3}} = \frac{(189)^{1/3}}{(7)^{1/3}} = \left(\frac{189}{7}\right)^{1/3} \]

5. **Simplifying the Ratio**:
- Calculate \( \frac{189}{7} = 27 \).
- Now, take the cube root: \( (27)^{1/3} = 3 \).

6. **Conclusion**: Therefore, the radius of the nucleus of Osmium is three times that of Lithium:
\[ R_{Os} = 3 \times R_{Li} \]

Thus, the correct answer is that the radius of the nucleus of Osmium is triple that of Lithium.