To determine the number of neutrons in the given element, we will follow these steps:
1. Identify the atomic number (Z): The atomic number is given as 92. This is the number of protons in the nucleus of the atom.
2. Identify the atomic mass (A): The atomic mass is given as 238. This represents the total number of protons and neutrons in the nucleus.
3. Calculate the number of neutrons (N): The number of neutrons can be found using the relationship:
[tex]\[ N = A - Z \][/tex]
where:
- [tex]\( A \)[/tex] is the atomic mass (238),
- [tex]\( Z \)[/tex] is the atomic number (92).
4. Perform the calculation:
[tex]\[ N = 238 - 92 \][/tex]
[tex]\[ N = 146 \][/tex]
So, the number of neutrons in the element [tex]\({ }_{92}^{238} U\)[/tex] is 146.
