Let's analyze the information given:
- The symbol for the radioactive nuclide is [tex]\({ }_{56}^{131} Ba\)[/tex].
From the notation [tex]\({ }_{56}^{131} Ba\)[/tex]:
1. The atomic number (denoted by the lower left subscript) is 56. This number represents the number of protons in the nucleus of the atom.
2. The mass number (denoted by the upper left superscript) is 131. This number represents the total number of protons and neutrons in the nucleus.
We are asked to verify the statements based on this information.
1. Statement: The atomic number of the radioactive nuclide is 75.
- Analysis: The atomic number is given as 56, not 75.
- Conclusion: This statement is incorrect.
2. Statement: The mass number of the radioactive nuclide is 131.
- Analysis: The symbol indicates a mass number of 131.
- Conclusion: This statement is correct.
3. Statement: The number of neutrons that are present in the nucleus of each atom is 56.
- Analysis: The number of neutrons can be calculated by subtracting the atomic number from the mass number:
[tex]\[
\text{Number of neutrons} = \text{Mass number} - \text{Atomic number} = 131 - 56 = 75
\][/tex]
This indicates the number of neutrons is 75, not 56.
- Conclusion: This statement is incorrect.
4. Statement: The number of protons that are present in the nucleus of each atom is 131.
- Analysis: The atomic number is the number of protons, which is 56, not 131.
- Conclusion: This statement is incorrect.
So, in summary and based on the given data:
- The atomic number of the radioactive nuclide is 56.
- The mass number of the radioactive nuclide is 131.
- The number of neutrons in the nucleus is 75.
- The number of protons is equal to the atomic number, which is 56.
Therefore, the only correct statement from the options given is:
The mass number of the radioactive nuclide is 131.
