The hydrogen atom contains 1 proton and 1 electron. The radius of the proton is approximately 1.0fm femtometers, and the radius of the hydrogen atom is approximately 53 pm (picometers).
- Calculate the volume of the nucleus and the volume of the atom for hydrogen.
- What percentage of the hydrogen atom's volume is occupied by the nucleus?
I'm still cannot figure it. Please help
Sure, I'd be happy to help! But before I do, let me just say that when it comes to physics, sometimes the numbers can be a bit nuclear. Alright, here we go:
To calculate the volume of the nucleus, we can use the formula for the volume of a sphere, which is V = (4/3)πr^3. Since the proton is at the center of the nucleus, we can consider the radius of the nucleus to be the radius of the proton. So, the volume of the nucleus would be (4/3)π(1.0fm)^3.
Now, to calculate the volume of the atom, we can use the same formula. The radius of the atom is given as 53 pm, so the volume would be (4/3)π(53pm)^3.
To find the percentage of the hydrogen atom's volume occupied by the nucleus, we can divide the volume of the nucleus by the volume of the atom, and then multiply by 100 to get the percentage. So, the percentage would be (volume of nucleus/volume of atom) * 100.
Now, let's do the math. Oh boy, I hope numbers don't explode in my face!
To calculate the volume of the nucleus and the volume of the hydrogen atom for hydrogen, we can use the formula for the volume of a sphere:
Volume of a sphere = (4/3) * π * r³
1. Volume of the nucleus:
Given that the radius of the proton is approximately 1.0 fm (femtometers), we can substitute this value into the formula:
Volume of the nucleus = (4/3) * π * (1.0 fm)³
Calculating this, we get:
Volume of the nucleus ≈ 4.19 fm³
2. Volume of the atom:
Given that the radius of the hydrogen atom is approximately 53 pm (picometers), we need to convert this value to femtometers (fm) before substituting it into the formula:
1 picometer (pm) = 0.01 femtometers (fm)
Converting the radius of the atom:
Radius of the atom = 53 pm * 0.01 fm/pm
Now, we can substitute this converted value into the formula:
Volume of the atom = (4/3) * π * (Converted radius of the atom)³
Calculating this, we get:
Volume of the atom ≈ 0.225 fm³
To find the percentage of the hydrogen atom's volume occupied by the nucleus, we can use the formula:
(Volume of the nucleus / Volume of the atom) * 100
Substituting the calculated values:
(4.19 fm³ / 0.225 fm³) * 100 ≈ 18.62%
Therefore, approximately 18.62% of the hydrogen atom's volume is occupied by the nucleus.
To calculate the volume of the nucleus and the volume of the atom for hydrogen, we can use the formula for the volume of a sphere:
Volume = (4/3) × π × radius^3
1. Volume of the nucleus:
The radius of the proton is given as approximately 1.0 fm (femtometers).
Convert the femtometer to meters: 1 fm = 1 × 10^-15 m.
Now we can calculate the volume of the nucleus:
Volume_nucleus = (4/3) × π × (radius_proton)^3
= (4/3) × π × (1 × 10^-15 m)^3
2. Volume of the atom:
The radius of the hydrogen atom is given as approximately 53 pm (picometers).
Convert the picometer to meters: 53 pm = 53 × 10^-12 m.
Now we can calculate the volume of the atom:
Volume_atom = (4/3) × π × (radius_atom)^3
= (4/3) × π × (53 × 10^-12 m)^3
To find the percentage of the hydrogen atom's volume occupied by the nucleus, we need to calculate the ratio of the nucleus volume to the atom volume.
Percentage = (Volume_nucleus / Volume_atom) × 100
Now let's plug in the values and calculate the answers.