Q1.
an atom had no empty space? How would this have affected the size of various objects?
Answer
Everything would shrink enormously — while keeping exactly the same mass.
How much? The nucleus is about 105 times smaller in diameter than the atom. If all the empty space were removed, every length would shrink by that factor, so every volume would shrink by its cube.
Length scale factor = 105
Volume scale factor = (105)3 = 1015
A cricket ball of diameter 7 cm would become
7 cm ÷ 105 = 7 × 10–5 cm = 0.7 µm — smaller than a speck of dust
Your body, about 1.6 m tall, would become
1.6 m ÷ 105 = 1.6 × 10–5 m = 16 µm — about the width of a single hair
Volume scale factor = (105)3 = 1015
A cricket ball of diameter 7 cm would become
7 cm ÷ 105 = 7 × 10–5 cm = 0.7 µm — smaller than a speck of dust
Your body, about 1.6 m tall, would become
1.6 m ÷ 105 = 1.6 × 10–5 m = 16 µm — about the width of a single hair
The mass, however, would be unchanged, so the density would go up by 1015. A cricket ball of 160 g compressed into 0.7 µm would still weigh 160 g. A teaspoon of such matter would weigh millions of tonnes.
Why it happens: almost all the mass of an atom is in the nucleus, and almost all the volume is in the electron region. Remove the electron region and you lose the volume but not the mass — that is the whole reason nuclear matter is so fantastically dense.
Did you know? This is not only a thought experiment. In a neutron star, gravity really does crush atoms until the nuclei touch. A neutron star packs more mass than the Sun into a ball roughly the size of a city.