Physicists mathematicians and others often deal with large...

Name: physicists mathematicians and others often deal with large numbers the number 10100 has been given the whimsical name googol by mathematicians let us compare some large numbers in physics wi 61904
Uploaded: 2020-08-29T23:58:16-08:00
Duration: 9 min 50 s
Channel: Guilherme Barros
Description: physicists mathematicians and others often deal with large numbers the number 10100 has been given the whimsical name googol by mathematicians let us compare some large numbers in physics wi 61904

Physicists, mathematicians, and others often deal with large numbers. The number 10100 has been given the whimsical name googol by mathematicians. Let us compare some large numbers in physics with the googol. (Note: This problem requires numerical values that you can find in the appendices of the book, with which you should become familiar.)Approximately how many neutrons are in a neutron star? Neutron stars are composed almost entirely of neutrons and have approximately twice the mass of the sun.

Transcript

00:01 In question a, we have to estimate the number of atoms that compose the earth.

00:07 And in order to do that, we have to use that the average atomic mass of atoms on the earth is 14 grams per mole.

00:24 Okay, so in order to do that, we need to first obtain the mass of the earth.

00:30 And we can simply look up in a table that the mass of the earth is approximately 6 times cents to the 24th kilograms.

00:42 Okay, which is the same as 6 times 10 to the 27 grams.

00:48 I just multiply the mass by 1 ,000.

00:52 Now, in order to obtain the number of malls that can pull the planet, we get that we have to divide the mass of the planet by the molar mass.

01:05 Of the average molar mass of the atoms that compose earth.

01:12 So we have six times 10 to the 27th grams divided by 14 grams per mole.

01:20 So we get the total number of malls that compose the earth is 4 .29 times 10 to the 26 malls.

01:35 Now one mall, let me write it right here, one mall, has 6 .02 times 10 to the 23rd atoms.

01:56 So we have to multiply 4 .29 times 10 to the 26 malls by 6 .02 times 10 to the 23rd atoms per mole.

02:16 So in the end, we have a total of 2 .58 times 10 to the 50th this is the answer to question a.

02:36 In question b, we have to calculate how many neutrons there are in a neutron star.

02:45 So, and we have to consider that the mass of the neutron star is two times the mass of the sun.

02:52 Now the mass of the sun, you can also look it up in a table, is approximately two times thin to the 30th kilograms.

03:02 So the mass of a neutron star is approximately four times.

03:06 Times 10 to the 30th kilograms.

03:12 And also notice that the mass of a single neutron is equal to 1 .67 times 10 to the minus 27 kilograms.

03:22 So we have to divide the total mass of the neutron star 4 times 10 to the 30th by the mass of a single newton, that's 1 .67, and 10 to the minus 27 kilograms per newton per neutrin, i'm sorry.

03:38 And this gives 2 .4 times cent of 57 neutrons.

03:49 So this is approximately the number of neutrons in a neutron star.

03:54 In question c, we have to consider the very early universe when the whole universe fits into the size of a sphere that has a radius that is equal to the distance between the earth and the sun.

04:12 At that time, the density of the universe was equal to 10 to 15 grams per cubic centimeter.

04:26 And we have to consider that the universe was composed 1 third of electrons, one third of protons, and one third of neutrons.

04:37 In that case, we have to calculate how many, particles composed the universe.

04:44 And in the density, it shouldn't be, but 10 to the 5, it should be 10 to the 15th...

Question

Please give Ace some feedback