A living specimen in equilibrium with the atmosphere contains one atom of 14C (h

Question

A living specimen in equilibrium with the atmosphere contains one atom of 14C (half-life = 5 730 yr) for every 7.70 × 1011 stable carbon atoms. An archeological sample of wood (cellulose, C12H22O11) contains 21.0 mg of carbon. When the sample is placed inside a shielded beta counter with 88.0% counting efficiency, 837 counts are accumulated in one week. Assuming that the cosmic-ray flux and Earth’s atmosphere have not changed appreciably since the sample was formed, as time passes which of the following is constant? A. The sum of the numbers of protons and neutrons in the sample B. the number of protons in the sample C. Both the number of neutrons and the number of protons in the sample D. The number of neutrons in the sample

Explanation / Answer

No calculations are required to answer this problem.

As we know, in beta-decay, mass number remains same and the atomic number is increases by one unit. What exactly happen in beta-decay is, "A neutron is changed into a proton."

Example:-    11Na24   --------> 12Mg24 + -1e0

Here in the example, number of protons on left side = 11, number of neutrons on left side = 24-11 = 13

so, the sum of numbers of protons and neutrons on left side = 11+13 = 24

number of protons on right side = 12

number of neutrons on right side = 24-12 = 12

sum of numbers of protons and numbers of neutrons = 12+12 = 24

So, It is clear from the example that the sum of the numbers of protons and neutrons in the sample remains constant.

Correct Choice is (A).

B) is not the correct choice since the number of protons is increased by 1 for each beta decay.

C) is not correct since the neutron is changed into proton, so the number of neutrons decreases and number of protons increases.

D) is not correct since neutrons are decreaes and changed into protons.

Hence, the only correct choice is (A).

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