Physicists estimate that there are between 1078 and 1082 atoms in the universe. How do these two numbers compare with one another? If the larger number is right, how many universes with the smaller number of atoms would fit inside the larger universe?

Physicists estimate that there are between 10^78 and 10^82 atoms in the universe. How do these two numbers compare with one another? If the larger number is right, how many universes with the smaller number of atoms would fit inside the larger universe?

Solution

To find the amount of the smaller number of atoms that will fit into the larger, we simply divide

Thus, we have;

10^82/10^78 = 10^4 = 10,000

MrRoyal MrRoyal · Answer 2 · 2021-10-26T14:23:32+02:00

Estimates are used to give the approximated value of a quantity.

10000 of the smaller universe will fit in the larger universe.

The number of atoms is:

[tex]\mathbf{n_1 = 10^{78}}[/tex]

[tex]\mathbf{n_2 = 10^{82}}[/tex]

(a) The larger universe

By comparison,

[tex]\mathbf{10^{82} > 10^{78}}[/tex]

This means that: the atoms in the second universe are larger than the number of atoms in the first.

(b) The number of small universe in the large universe

This is calculated by dividing the number of atoms in the large universe by the small universe

So, we have:

[tex]\mathbf{n = \frac{n_2}{n_1}}[/tex]

[tex]\mathbf{n = \frac{10^{82} }{ 10^{78}}}[/tex]

Apply law of logarithm

[tex]\mathbf{n = 10^{82 - 78} }[/tex]

[tex]\mathbf{n = 10^{4} }[/tex]

[tex]\mathbf{n = 10000 }[/tex]

Hence, 10000 of the smaller universe will fit in the larger universe.