The half-life of radium is 1600 years. The number of atoms...

The half-life of radium is 1600 years. The number of atoms that will decay from $1 \mathrm{~g}$ sample of radium per second is (Given: Atomic weight of radium $=226$ ) :
(a) $3.6 \times 10^{10}$
(b) $7.2 \times 10^{10}$
(c) $4.2 \times 10^{10}$
(d) $14.6 \times 10^{10}$

Key Concepts

Mole and Avogadro's Number

The mole is a standard unit in chemistry that represents a specific number of particles, defined by Avogadro's number (approximately 6.022 × 10^23). This concept is essential for converting between mass and the number of atoms or molecules, enabling quantitative analysis of substances at the atomic scale.

Activity

Activity is a measure of the number of decays per unit time in a radioactive sample, usually expressed in becquerels (decays per second). It is calculated by multiplying the decay constant by the number of radioactive atoms present, linking the microscopic decay process to a macroscopic observable quantity.

Half-Life

Half-life is the period required for half of the radioactive nuclei in a sample to decay. It is an intrinsic property of each radioactive isotope and governs the rate at which the number of unstable atoms decreases over time.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a nucleus will decay. It is directly related to the half-life via the relation ? = ln(2) / T½, and is used in the mathematical modeling of radioactive decay processes.

Radioactive Decay Law

The radioactive decay law describes the exponential decrease in the number of undecayed nuclei over time, expressed by the formula N(t) = N0 e^(–?t), where N0 is the initial number of atoms and ? is the decay constant. This law is fundamental in predicting the behavior of radioactive substances.

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