Phosphorus-32 2 is a commonly used radioactive nuclide in...

Phosphorus-32 2 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus- 32 is left from an original sample of 175 $\mathrm{mg}$ $\mathrm{Na}_{3}^{32} \mathrm{PO}_{4}$ after 35.0 days? Assume the atomic mass of $^{32} \mathrm{P}$ is 32.0 $\mathrm{u} .$

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Key Concepts

Radioactive Decay

Radioactive decay is the spontaneous process by which unstable atomic nuclei lose energy by emitting radiation. This decay follows an exponential law over time, and it is a fundamental concept in nuclear physics, affecting how materials and isotopes change as they release particles or energy.

Half-life

Half-life is the period required for half of a sample of a radioactive substance to decay. It is an intrinsic property of an isotope and serves as a critical measure for predicting how much of a radioactive sample remains after a given time, regardless of the initial quantity.

Exponential Decay Equation

The exponential decay equation, typically represented as N = N0 × (1/2)^(t/T1/2), quantifies the amount of a radioactive material left after a certain time (t) based on its initial quantity (N0) and its half-life (T1/2). This equation is essential for solving problems involving time-dependent nuclear decay.

Molar Mass and Isotopic Mass

Molar mass and isotopic mass are key in converting between the amount (in moles or atoms) and the mass of a substance. When dealing with radioactive decay, knowing the mass of the specific isotope allows one to accurately determine the remaining mass of the isotope after decay.

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