The diameter of a certain atomic nucleus is 2.60 x 10-3 pm and its mass is 3.40 x 10-23 g.?

Question

The diameter of a certain atomic nucleus is 2.60 x 10-3 pm and its mass is 3.40 x 10-23 g. What is the density of the nucleus in grams per centimeter cubed? Assume the nucleus is a sphere with a volume equal to 4/3 π r3

To enter a number in exponential notation use an e for the exponent, e.g., 2.34 x 106 enter as 2.34e6 2.34 x 10-16 enter as 2.34e-16

Answer 1

The density of an object is its mass divided by its volume.

1 pm = 1 picometer = 1e-12 meter = 1e-10 cm, so the radius of the nucleus is 1.30e-13 cm.

The volume of this nucleus is:

pi*(4/3)*r^3 = pi*(4/3) * (1.30e-13 cm)^3 = 9.203e-39 cm^3

Divide this volume into the mass to get the density:

(3.40e-23 gm)/(9.203e-39 cm^3) = 3.695e15 gm/cm^3

As the previous answerer indicated (though he/she got the wrong answer) the nucleus is *extremely* dense. Normal solid matter has a density in the range of about 1 to 10 gm/cm^3, so the nucleus is about 15 orders of magnitude (a quadrillion times) more dense than anything you are familiar with in everyday life.

Answer 2

1) You must convert 1.2x10^-3 pm into cm, since the question asks for the density of the nucleus in grams per centimeter cubed. Which is 1.2x10^-13 cm. 2) It gives you the diameter but you need the radius, so divide it by 2 because (radius=diameter/2). Then just plug it into the formula 4/3 Pi r^3. Which gives you a volume of 7.24 x 10^-39. 3) In order to get density take the mass and divide it by the volume. And the answer should be 8.4 x 10^15. I think that's the right answer. Check my math but that's the way you do it. Good Luck =)

Answer 3

I agree broadly with the other two answerers, who have both used the correct logic except for rhsaunders at the final step (I think what happened is that he/she divided V by m (giving 2.7×10^-16) and dropped the negative sign on the exponent; the correct answer is the reciprocal of this.) However, neither of them paid attention to the correct number of significant figures.

1 pm = 10^-12 m = 10^-10 cm, so the diameter is 2.60×10^-13 cm and the radius is 1.30×10^-13 cm.

V = 4/3 π r^3 = 1/6 π d^3 = 9.203×10^-39 cm^3
ρ = m / V = 3.40×10^-23 / 9.203×10^-39
= 3.69×10^15 g/cm^3.

Answer 4

The volume, in terms of diameter, is pi d^3/6, so we have v = pi (2.6E-13)^3/6 = 9.1981E-39 cm^3. Dividing by 3.4E-23 grams gives us 2.7E16 grams per cubic centimeter. Don't drop it on your toe.