Let's carefully analyze the information provided to determine the correct symbol for this isotope of uranium.
1. Mass Number (A) and Atomic Number (Z):
- The mass number (A) is the total number of protons and neutrons in the nucleus. For this isotope, the mass number is 238.
- The atomic number (Z) is the number of protons in the nucleus, which uniquely identifies the element. For this isotope of uranium, the atomic number is 92.
2. Symbol Representation:
- The conventional way to represent an isotope involves both the mass number and the atomic number. The format typically used is [tex]\({ }_{Z}^{A} \text{Element Symbol}\)[/tex], where [tex]\(Z\)[/tex] is the atomic number, [tex]\(A\)[/tex] is the mass number, and the element symbol is the symbol of the element.
3. Element Symbol:
- Uranium is represented by the symbol [tex]\( \text{U} \)[/tex].
Using the given values:
- Mass number [tex]\(A = 238\)[/tex]
- Atomic number [tex]\(Z = 92\)[/tex]
- Element symbol [tex]\( \text{U} \)[/tex]
The correct notation would be:
[tex]\[ { }_{92}^{238} \text{U} \][/tex]
4. Evaluating the Options:
- [tex]\( 924 \)[/tex] does not provide a clear or conventional representation of the isotope.
- [tex]\( 238 \; 92 \)[/tex] is also not in the correct notation format.
- [tex]\({ }^{92} \text{U} \)[/tex] specifies the atomic number but omits the mass number, making it incomplete.
Therefore, the best representation of this isotope of uranium, encompassing all the necessary information, is:
[tex]\[ { }_{92}^{238} \text{U} \][/tex]
So, the final answer is:
[tex]\[ { }_{92}^{238} \text{U} \][/tex]
