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Fundamentals Of Physics
Found in: Page 1363

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Short Answer

Certain theories predict that the proton is unstable, with a half-life of about 1032 years. Assuming that this is true, calculate the number of proton decays you would expect to occur in one year in the water of an Olympic-sized swimming pool holding 4.32 x 105L of water.

The number of proton decays is 1decayyear

See the step by step solution

Step by Step Solution

Step 1: Identifying the data given in the question

Given in the question

The half-life of a proton T1/2 = 1032 years

The volume of the pool, V = 4.32 x 105 L

We know

The density of the water,

ρ = 1000 kg/m3 = 1kg/L

Mass of the proton, mp = 1.67 x 10-27 kg

Step 1: Concept used to solve the question 

  • Radioactive Decay

Most of the known nuclides are radioactive. they spontaneously decay at a rate proportional to the number N of radioactive atoms present.

  • The half-life of a radioactive nuclide is the time required

for the decay rate R (or the number N) in a sample to

drop to half of its initial value.

Step 2: Calculating the number of proton decays

The total mass of the pool

Mpool=ρν = (4.32×105L)(1kg/L) = 4.32×105 kg

Since we know, by counting the protons versus total nucleons in a water molecule the fraction of that mass made up by the protons is1018.


the number of particles susceptible to decay is

localid="1663253177640" N =(10/18)Mpoolmp = (10/18)(4.32×105kg)mp=1.67×10-27kg = 1.44×1032

We know the rate of radioactive decay can be given as


Where R is the rate of decay, N is the number of particles susceptible to decay, T1/2and the half-life.


substituting the values into the formula.

localid="1663253193460" R=1.44×1032ln21032years=1decayyear

Hence the number of protons decay is1decayyear

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