## Answer :

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]