# Mass of Hydrogen needed to determine lifetime of proton

• MxwllsPersuasns
In summary, the current limit on the proton's lifetime is determined by observing a large body of water for 10 years and noticing no decay of hydrogen nuclei in H2O. The equation N = N0e-t/τ can be used to find the amount of protons needed, and from there the number of molecules and molecular weight can be calculated. However, the observation time is so small compared to the lifetime that this simplified equation may be used.
MxwllsPersuasns

## Homework Statement

The current limit on the proton’s lifetime is determined by observing a large body of water for a long time and noticing that no one of the hydrogen nuclei in H2O have decayed. Assuming that the experiment making this measurement has been going on for 10 years, how many tons of water are needed to set the constraint on the lifetime of the proton τ > 1034 years?

N = N0e-t/τ

## The Attempt at a Solution

For this I would think we would use this equation to then find the amount of protons needed to make -t/τ = -(10)/(1034 and then from that figure out the number of protons in H2O and then figure out how many molecules then multiply by the molecular weight. Am I on the right track?

That will work. You don't even need the full exponential function as the observation time is so tiny compared to the lifetime.

If you expect one decay (at a given lifetime value) and observe no decay, that is not sufficient to rule out this value (you could have been just a bit unlucky), but that is probably a technical detail you don't have to worry about here.

## 1. What is the significance of determining the mass of hydrogen in relation to the lifetime of a proton?

The mass of hydrogen is directly related to the mass of a proton, as a proton is the nucleus of a hydrogen atom. Therefore, by measuring the mass of hydrogen, we can indirectly determine the mass of a proton. This is important because the mass of a proton is a fundamental physical constant that affects many aspects of our understanding of the universe.

## 2. How is the mass of hydrogen measured?

The mass of hydrogen can be measured using various techniques, such as mass spectrometry or nuclear magnetic resonance. These methods involve ionizing the hydrogen atoms and measuring their mass-to-charge ratio or their resonance frequency, respectively.

## 3. Can the mass of hydrogen vary over time?

No, the mass of hydrogen is considered a constant value and is not expected to change over time. However, the accuracy of our measurement techniques and instruments may improve over time, leading to more precise values for the mass of hydrogen and thus the mass of a proton.

## 4. How does the mass of hydrogen affect the lifetime of a proton?

The mass of a proton is a crucial factor in determining the stability and lifetime of a proton. The lower the mass of a proton, the more stable it is, and the longer its lifetime is expected to be. Therefore, accurately measuring the mass of hydrogen can provide insights into the lifetime of a proton.

## 5. What other factors can affect the lifetime of a proton?

Aside from the mass of a proton, other factors that can affect its lifetime include the strength of the strong nuclear force, the presence of other particles, and the overall energy state of the proton. Studying the mass of hydrogen can help us understand how these factors interact and contribute to the stability of a proton.

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