Chapter 12, Problem 4C

### Inquiry into Physics

8th Edition
Ostdiek
ISBN: 9781337515863

Chapter
Section

### Inquiry into Physics

8th Edition
Ostdiek
ISBN: 9781337515863
Textbook Problem

# If the average lifetime of the proton were 10 years, estimate the number of protons per kilogram of human body mass that would decay radioactively each year. Assume that a human being is made entirely of water molecules and that each molecule contributes 10 protons. (Hint: The molar weight of water is 18 g, and each mole of any substance contains particles.) If each proton decay released 1 MeV of energy, how much energy per kilogram would be produced in total by the decaying protons in your body in 1 year? Give the result in joules per kilogram. If the energy released is mostly in the form of kinetic energy of the positrons produced in the decay, then 1 J/kg of this type of ionizing radiation is rated at about 1 Sv (the sievert [Sv] is the SI unit of radiation dose). Compare the total exposure in sieverts of a person to the radiation produced by his/her own body to the maximum safe dose of 1 mSv/yr for the general public from all artificial sources.

To determine

The number of protons per kg of human body, energy per kilogram b decaying proton.

Explanation

Given:

Average life time, tm=1016years

Molar mass of water, M = 18g.

Calculation:

The average life time of proton is given by,

tm=1Î»Î»=1tm

The number of protons at time tm is given by,

N(tm)=N0eâˆ’Î»tm

N0 = number of protons initially

N(tm) = number of protons at time t,

The number of protons initially is,

N0=100018Ã—10=555proton

The number of protons at time tm is given by,

N(tm)=N0eâˆ’Î»tmN(tm)=555Ã—0.37N(tm)â‰ˆ205

Thus, number of proton decay in a year is,

N0âˆ’N(tm)=555âˆ’205=350

One decay proton releases 1MeV of energy

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