find the scale factor - If the size of a nucleus (in the range of 10^{-15} \text{ to } 10^{-14} m ) is scaled up to the tip of a sharp pin, what roughly is the size of an atom ? Assume tip of the pin to be in the range 10^{-5} m \text{ to } 10^{-4} m .

If the size of a nucleus (in the range of 10^{-15} \text{ to } 10^{-14} m ) is scaled up to the tip of a sharp pin, what roughly is the size of an atom ? Assume tip of the pin to be in the range 10^{-5} m \text{ to } 10^{-4} m .

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Guru Nanak (last edited 2 years ago) (Student, UG2 Grade)

Given that

Size of range the nucleus = 10^{-15} \text{ to } 10^{-14} m

Tip of the pin = 10^{-5} \text{ to } 10^{-4} m

Actual size of the nucleus = 10^{-10} m

Imaginary figure:

Step 1: Calculating the scaling factor of the nucleus

\text{ Scaling factor }=\frac{\text{ New size of the nucleus }}{\text{ Original size of nucleus }}

= \frac{10^{-5}}{10^{-15}}

= 10^{10}

Hence, scaling up by a factor of = 10^{10} m

Step 2: Finding the nucleus's approximate size?

\text{ approximate size } = \text{ scale factor * Actual size }

\text{ approximate size } = 10^{-10}* 10^{10}

\text{ approximate size } = 1

Hence, nucleus's approximate size 1 m