The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.0 10-15 m. The single electron in a hydrogen atom normally orbits the nucleus at a distance of 5.3 10-11 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom?

(density of nucleus / density of atom)

density = mass/volume
Use the exact mass of the H atom (and is this protium or all of the isotopes averaged?). You are given th volume. Calculate density of the nucleus from these values.

For the entire atom, add the mass of the electron to the mass of the proton you have used from above, and divide that combined mass by the volume listed in the problem. Calculate the density of the atom. Note: You aren't give the volume but the radius. Volume of sphere = 4/3*pi*r3.
Finally, commpute the ratio as you have noted.

The volume of a sphere is
(4/3)*pi*r3.

Explain Bot Explain Bot answered
8 months ago

To calculate the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom, we need to follow these steps:

1. Calculate the density of the nucleus:
- The radius of the nucleus is given as 1.0 x 10^(-15) m.
- The volume of a sphere is (4/3) * pi * r^3, where r is the radius.
- Use this formula to calculate the volume of the nucleus.
- The nucleus contains a single proton, and the exact mass of a proton is 1.673 x 10^(-27) kg.
- Divide the mass of the proton by the volume of the nucleus to calculate the density of the nucleus.

2. Calculate the density of the complete hydrogen atom:
- The radius of the electron orbit is given as 5.3 x 10^(-11) m.
- Use the volume formula for the electron orbit to calculate the volume of the atom.
- Add the mass of the proton (1.673 x 10^(-27) kg) and the mass of the electron (9.109 x 10^(-31) kg) to get the total mass of the atom.
- Divide the total mass by the volume of the atom to calculate the density of the atom.

3. Calculate the ratio of the density of the nucleus to the density of the atom:
- Divide the density of the nucleus by the density of the atom to get the ratio.

Remember to substitute the appropriate values and units (meters and kilograms) into the calculations to obtain the correct results.

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