# The density of a proton (hydrogen nucleus)

• mrcake
In summary, the conversation discusses calculating the volume and density of a proton using the formula V = 4/3 x pi x r^3 and D = m/V. The final result is a density of 2.3 x 10^17 kg/m^3, which is questioned for its meaning and relevance.
mrcake
Homework Statement
A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 x 10^-27 kg. Determine the density of the proton
Relevant Equations
D = m/V
First of all i want is to check if my answer is right or not because i am really not sure about my answer.
Because the length is given in the form of a diameter we will divide that by 2 so we get it in the form of radius,
2.4fm / 2 = 1.2fm = r
Then we will convert the radius from "fm" to "m" so we that'll be,
r = 1.2 x 10^-15 m.
so we now have the radius in meters and from that we can calculate the volume of the proton, by the following formula V = 4/3 x pi x r^3
V = 4/3 x pi x (1.2 x 10^-15)^3 = 7.23 x 10^-45 m^3
Since we have the mass and we calculated the volume we can plug them into formula of density so we'll get,
D = m/V
D = 1.67 x 10^-27 / 7.23 x 10^-45 = 2.3 x 10^17 kg/m^3

Something is not right with your answer. Take a good look at it. Hint: Water has density 1000 kg/m3.

hi thanks for reply, but what does water have to do with the proton of the hydrogen atom

PeroK
How many protons does a glass of water (0.25 L) contain? What would be the mass of that glass of water if your number for the density is correct?

kuruman said:
How many protons does a glass of water (0.25 L) contain? What would be the mass of that glass of water if your number for the density is correct?
Water is mostly space. A single proton may have a huge classical density - compare with a neutron star, for example.

mrcake said:
D = 1.67 x 10^-27 / 7.23 x 10^-45 = 2.3 x 10^17 kg/m^3
Looks about right given the numbers.

mrcake
PeroK said:
Looks about right given the numbers.
Is it right?

mrcake said:
Is it right?
Google thinks it's right to within an order of magnitude.

mrcake said:
Is it right?
It seems a fairly meaningless number, if you ask me. The density of water or hydrogen gas is meaningful; but the density of an elementary particle, given that it isn't actually a solid, localised sphere seems a pointless calculation. Sorry for the philosophical answer.

berkeman

## 1. What is the density of a proton?

The density of a proton, also known as the hydrogen nucleus, is approximately 2.7 x 10^14 grams per cubic centimeter.

## 2. How does the density of a proton compare to other particles?

The density of a proton is significantly higher than other subatomic particles, such as electrons, which have a density of approximately 2.8 x 10^-4 grams per cubic centimeter.

## 3. How is the density of a proton calculated?

The density of a proton is calculated by dividing its mass by its volume. The mass of a proton is approximately 1.67 x 10^-24 grams and its volume is approximately 1.67 x 10^-45 cubic centimeters.

## 4. Does the density of a proton change in different environments?

No, the density of a proton remains constant regardless of its environment. However, its mass and volume may change due to interactions with other particles.

## 5. Why is the density of a proton important in scientific research?

The density of a proton is important in understanding the structure and behavior of atoms and molecules. It also plays a crucial role in fields such as nuclear physics and astrophysics.

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