The time required for the decay of radium-223 from a concentration of 0.24 0 mol to 1.50 × 10 − 2 mol , with a half-life of 11.4 days is to be determined. Concept introduction: The half-life of a substance is the numerical value in which the given radioactive substance is assumed to be reduced to half of its initial number. The half-life for a given substance is represented by t 1/2 . In case, the decay of a radioactive substance is exponential, it will remain constant for the life time of the substance. After each half-life period, the amount of the substance is reduced to half of the initial number. The time required for the decay of the substance to a given amount of substance can be calculated using the formula mentioned below: ln ( N t N 0 ) = − kt In the above equation, ‘N t ’ represents the mass of the radioactive substance after a certain time interval t, ‘N 0 ’ indicates the initial mass of the radioactive material, ‘k’ represents the decay constant and ‘t’ represents the time interval for the half-life (t 1/2 ).

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Chapter 17, Problem 72E

Interpretation Introduction

Interpretation:

The time required for the decay of radium-223 from a concentration of 0.240 mol to 1.50×10−2 mol, with a half-life of 11.4 days is to be determined.

Concept introduction:

The half-life of a substance is the numerical value in which the given radioactive substance is assumed to be reduced to half of its initial number. The half-life for a given substance is represented by t_1/2.

In case, the decay of a radioactive substance is exponential, it will remain constant for the life time of the substance.

After each half-life period, the amount of the substance is reduced to half of the initial number.

The time required for the decay of the substance to a given amount of substance can be calculated using the formula mentioned below:

ln(NtN0)=−kt

In the above equation, ‘N_t’ represents the mass of the radioactive substance after a certain time interval t, ‘N₀’ indicates the initial mass of the radioactive material, ‘k’ represents the decay constant and ‘t’ represents the time interval for the half-life (t_1/2).

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