It really depends on what you mean by universe, but you certainly cannot actually prove it is infinite in any case. Generally people mean the observable universe, even assuming they know there were other definitions of "universe".
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· 9 years ago
The space in the universe is believed to be infinite, not the matter in it.
FALSE
Lets give a generously large estimate for the size of a grain of sand at 2mm (0.2 cm) diameter. Assume a spherical grain of sand (which is again, generously large) and calculate volume:
(4/3)*pi*(0.1cm)^3 = 4.19E-3 cc (cc= cubic centimeter)
The density of quartz (what sand is made of) is 2.65 g/cc so
(4.19E-3 cc)*(2.65 g/cc)= 1.11E-2 g
Silicon dioxide (quartz) has a formula mass of 60.08 g/mol so
(1.11E-2g)/(60.08 g/mol)= 1.84E-4 moles of SiO2
Each mole of SiO2 has 3 moles of atoms so
(1.84E-4)*3= 5.54E-4 moles of atoms
One mole is 6.022E23 atoms so
(5.54E-4 moles)*(6.022E23 atoms) = 3.33E20 atoms per grain of sand
The number of stars in the observable universe is estimated at 1E29.
3.33E20 < 1E29
There are not more atoms in a grain of sand than stars in the universe.
QED.
Lets give a generously large estimate for the size of a grain of sand at 2mm (0.2 cm) diameter. Assume a spherical grain of sand (which is again, generously large) and calculate volume:
(4/3)*pi*(0.1cm)^3 = 4.19E-3 cc (cc= cubic centimeter)
The density of quartz (what sand is made of) is 2.65 g/cc so
(4.19E-3 cc)*(2.65 g/cc)= 1.11E-2 g
Silicon dioxide (quartz) has a formula mass of 60.08 g/mol so
(1.11E-2g)/(60.08 g/mol)= 1.84E-4 moles of SiO2
Each mole of SiO2 has 3 moles of atoms so
(1.84E-4)*3= 5.54E-4 moles of atoms
One mole is 6.022E23 atoms so
(5.54E-4 moles)*(6.022E23 atoms) = 3.33E20 atoms per grain of sand
The number of stars in the observable universe is estimated at 1E29.
3.33E20 < 1E29
There are not more atoms in a grain of sand than stars in the universe.
QED.
(Justification for size of sand grain: http://en.wikipedia.org/wiki/File:Wentworth-Grain-Size-Chart.pdf)