To determine which of the provided statements about the radioactive nuclide [tex]\(\ce{_{56}^{131}Ba}\)[/tex] is correct, we can analyze each statement based on the properties of the nuclide. Here's the step-by-step analysis:
1. Atomic Number and Mass Number:
- The symbol [tex]\(\ce{_{56}^{131}Ba}\)[/tex] tells us that the atomic number ([tex]\(Z\)[/tex]) is 56. This number indicates the number of protons in the nucleus.
- The mass number ([tex]\(A\)[/tex]) is 131. This number is the sum of protons and neutrons in the nucleus.
2. Calculating the Number of Neutrons:
- The number of neutrons ([tex]\(N\)[/tex]) in the nucleus can be calculated using the formula:
[tex]\[
N = A - Z
\][/tex]
Substituting the known values:
[tex]\[
N = 131 - 56 = 75
\][/tex]
Therefore, there are 75 neutrons in the nucleus of [tex]\(\ce{_{56}^{131}Ba}\)[/tex].
3. Evaluating Each Statement:
- Statement 1: The atomic number of the radioactive nuclide is 75.
[tex]\[
\text{This statement is false because the atomic number is 56, not 75.}
\][/tex]
- Statement 2: The mass number of the radioactive nuclide is 131.
[tex]\[
\text{This statement is true because the mass number is indeed 131.}
\][/tex]
- Statement 3: The number of neutrons that are present in the nucleus of each atom is 56.
[tex]\[
\text{This statement is false because the number of neutrons is 75, not 56.}
\][/tex]
- Statement 4: The number of protons that are present in the nucleus of each atom is 131.
[tex]\[
\text{This statement is false because the number of protons is 56, not 131.}
\][/tex]
After evaluating all statements, we conclude that:
- The only correct statement is: The mass number of the radioactive nuclide is 131.
Thus, among the provided statements, Statement 2 is the correct one.
