To determine which statement is correct regarding the radionuclide used to diagnose lymphoma, let's analyze the given information step by step:
1. Number of Protons:
- It is given that the atom of this radionuclide contains 31 protons.
- The number of protons determines the atomic number of an element. Therefore, the atomic number is 31.
2. Number of Neutrons:
- It is given that the atom contains 36 neutrons.
3. Mass Number:
- The mass number is the total number of protons and neutrons in the nucleus of an atom.
- Mass Number = Number of Protons + Number of Neutrons
- Mass Number = 31 (protons) + 36 (neutrons) = 67.
4. Chemical Symbol:
- The given atomic number matches Gallium (Ga) in the periodic table.
- The notation for isotopes includes the atomic number as a subscript and the mass number as a superscript before the chemical element symbol.
- Therefore, the correct notation for this radionuclide is [tex]\(\mathrm{{}_{31}^{67} Ga}\)[/tex].
Considering the points above, let's evaluate the given statements one by one:
1. The atomic number is 31, the mass number is 67, and its symbol is [tex]\(\mathrm{{}_{31}^{67} Ga}\)[/tex]:
- This is correct based on our derived atomic number, mass number, and isotope symbol.
2. The atomic number is 31, the mass number is 67, and its symbol is [tex]\(\mathrm{{}_{67}^{31} Ga}\)[/tex]:
- This is incorrect since the mass number should be the superscript and the atomic number should be the subscript.
3. The atomic number is 67, the mass number is 31, and its symbol is [tex]\(\mathrm{{}_{31}^{67} Ga}\)[/tex]:
- This is incorrect because the atomic number should be 31, not 67, and the mass number should be 67, not 31.
4. The atomic number is 67, the mass number is 31, and its symbol is [tex]\(\mathrm{{}_{67}^{31} Ga}\)[/tex]:
- This is incorrect for the same reason as the previous statement; the atomic number and mass number are wrongly positioned.
The correct statement about the radionuclide is:
The atomic number is 31, the mass number is 67, and its symbol is [tex]\(\mathrm{{}_{31}^{67}} Ga\)[/tex].
This concludes our detailed step-by-step analysis and verification.
