The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0 x 10^-13 cm. The hydrogen atom itself has a radius of approximately 52.9 pm. What fraction of the space within the atom is occupied by the nucleus.
1E-13 cm = ? pm
(? pm/52.9) = ? as a fraction.
1.9*10^-5
bbb
To find the fraction of space occupied by the nucleus within the atom, we can compare the volumes of the nucleus and the entire atom.
The volume of the nucleus can be calculated using the formula for the volume of a sphere:
Volume_nucleus = (4/3) * π * (radius_nucleus)^3
Substituting the given radius_nucleus of 1.0 x 10^-13 cm, we can calculate the volume of the nucleus.
Next, we need to calculate the volume of the atom. The radius of the atom is given as 52.9 pm (picometers), so we need to convert this to cm by dividing by 100:
radius_atom = 52.9 pm ÷ 100 = 0.529 x 10^-9 cm
The volume of the atom is also calculated using the formula for the volume of a sphere:
Volume_atom = (4/3) * π * (radius_atom)^3
Now we have both the volume of the nucleus and the volume of the atom. To find the fraction of space occupied by the nucleus within the atom, we divide the volume of the nucleus by the volume of the atom:
Fraction_nucleus = Volume_nucleus / Volume_atom
By plugging in the calculated values, you can find the fraction of space occupied by the nucleus within the atom.