To solve the problem, we will break it down step-by-step, based on the information given:
1. Given Information:
- The radius of the atom is [tex]\(2 \, \text{Å}\)[/tex] (Angstroms).
- The radius of the nucleus is related to the radius of the atom by a factor of [tex]\(y \times 10^{-15}\)[/tex].
2. Determining the Radius of the Nucleus:
The radius of the nucleus is obtained by multiplying the radius of the atom by the given factor [tex]\(y \times 10^{-15}\)[/tex]:
[tex]\[
\text{Radius of the nucleus} = 2 \, \text{Å} \times (10^{-15})
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Radius of the nucleus} = 2 \times 10^{-15} \, \text{Å}
\][/tex]
3. Possible Values for [tex]\(y\)[/tex]:
We need to determine which of the given choices for [tex]\(y\)[/tex] results in the correct radius of the nucleus:
- Option 1: [tex]\(y = 4\)[/tex]
- Option 2: [tex]\(y = 8\)[/tex]
4. Checking Each Option:
Let's test each option to see if it satisfies the given conditions:
- If [tex]\(y = 4\)[/tex]:
[tex]\[
\text{Radius of the nucleus} = 4 \times 10^{-15} \, \text{Å}
\][/tex]
This does not match [tex]\(2 \times 10^{-15} \, \text{Å}\)[/tex], so [tex]\(y\)[/tex] cannot be 4.
- If [tex]\(y = 8\)[/tex]:
[tex]\[
\text{Radius of the nucleus} = 8 \times 10^{-15} \, \text{Å}
\][/tex]
This also does not match [tex]\(2 \times 10^{-15} \, \text{Å}\)[/tex], so [tex]\(y\)[/tex] cannot be 8 either.
Thus, neither of the given options correctly fits the condition for the nucleus radius based on the problem's description. Therefore, the answer for this problem is:
[tex]\[
\boxed{\text{None}}
\][/tex]
