(41) The average diameter of an atom's nucleus is about \( 1 \times 10^{-14} \) meter. The diameter of a proton is about \( 1 \times 10^{-15} \) meter. (4). The diameter of a proton times 10 roised to what power is equivalent to the diameter of a nucleus?

To find the power to which we need to raise 10 in order to express the diameter of a nucleus in terms of the diameter of a proton, we can set up the following relationship: 1. The diameter of a proton is \( 1 \times 10^{-15} \) meters. 2. The diameter of a nucleus is \( 1 \times 10^{-14} \) meters. We can express the diameter of the nucleus in terms of the diameter of the proton: \[ \text{Diameter of nucleus} = k \times \text{Diameter of proton} \] where \( k \) is a constant. Substituting the values we have: \[ 1 \times 10^{-14} = k \times 1 \times 10^{-15} \] To find \( k \), we can divide both sides by \( 1 \times 10^{-15} \): \[ k = \frac{1 \times 10^{-14}}{1 \times 10^{-15}} = 10^{(-14) - (-15)} = 10^{1} \] Thus, \( k = 10^1 \). This means that the diameter of a nucleus is equivalent to the diameter of a proton multiplied by \( 10^1 \). Therefore, the answer is: \[ \text{The diameter of a proton times } 10^1 \text{ is equivalent to the diameter of a nucleus.} \]