Question

lets make this more visual using information from the chart of fundamental particles. if the proton were 10 cm in diameter... the size of an orange, how big would everything be? the atom is often represented as a miniature ___________ ___________. draw it:

Explanation:

Step1: Find the scale factor

The scale factor \(k\) is found by dividing the model size of the proton by its actual size.
The actual size of the proton \(a_p = 10^{- 15}\text{ m}\) and the model size \(m_p=10\text{ cm}=0.1\text{ m}\)
\(k=\frac{m_p}{a_p}=\frac{0.1}{10^{-15}} = 10^{14}\)

Step2: Calculate the model size of the neutron

Since the actual size of the neutron \(a_n = 10^{-15}\text{ m}\)
The model size \(m_n=k\times a_n\)
\(m_n = 10^{14}\times10^{-15}=1\text{ cm}\) (a small grape - like object)

Step3: Calculate the model size of the electron

The actual size of the electron \(a_e=10^{-18}\text{ m}\)
The model size \(m_e=k\times a_e\)
\(m_e=10^{14}\times10^{-18}=10^{-4}\text{ m} = 0.1\text{ mm}\) (a speck of dust)

Step4: Calculate the model size of the atom

The actual size of the atom \(a_{at}=10^{-10}\text{ m}\)
The model size \(m_{at}=k\times a_{at}\)
\(m_{at}=10^{14}\times10^{-10}=10^{4}\text{ m}=10\text{ km}\) (a small city - like scale, and the atom is often represented as a miniature solar - system)

Answer:

object	actual size	model size	model
neutron	\(10^{-15}\text{ m}\)	\(1\text{ cm}\)	small grape
electron	\(10^{-18}\text{ m}\)	\(0.1\text{ mm}\)	speck of dust
atom	\(10^{-10}\text{ m}\)	\(10\text{ km}\)	small city (solar - system)