Let's analyze the process of alpha decay step by step. In alpha decay, an alpha particle, which consists of 2 protons and 2 neutrons, is emitted. This type of particle has an atomic number of 2 (represented by [tex]\( _2^4 He \)[/tex]) and a mass number of 4.
We start with Uranium-238, which has:
- An atomic number of 92 (92 protons)
- A mass number of 238 (total of protons and neutrons)
When Uranium-238 emits an alpha particle, it loses 2 protons and 2 neutrons. To find the new isotope formed, we subtract these amounts from Uranium-238:
1. Calculate the new atomic number:
[tex]\[
\text{New atomic number} = \text{Initial atomic number} - \text{Alpha particle's atomic number}
\][/tex]
[tex]\[
\text{New atomic number} = 92 - 2 = 90
\][/tex]
2. Calculate the new mass number:
[tex]\[
\text{New mass number} = \text{Initial mass number} - \text{Alpha particle's mass number}
\][/tex]
[tex]\[
\text{New mass number} = 238 - 4 = 234
\][/tex]
So, the resulting isotope will have:
- An atomic number of 90
- A mass number of 234
The element with an atomic number of 90 is Thorium (Th).
Therefore, the isotope formed is:
[tex]\[
_{90}^{234} Th
\][/tex]
Hence, the correct answer is:
B. [tex]\({ }_{90}^{234} Th\)[/tex]
