A fission reactor is hit by a missile, and 5.00 ×10^6 Ci of 90 Sr, with half-life 27.7 yr, evapo

step 1 Hi friends, here it is given a missile hitting the fizzle reactor which having activity 5 into 1

A fission reactor is hit by a missile, and 5.00 ×10^6 Ci of...

A fission reactor is hit by a missile, and $5.00 \times 10^{6} \mathrm{Ci}$ of 90 Sr, with half-life 27.7 yr, evaporates into the air. The strontium falls out over an area of $10^{4} \mathrm{km}^{2} .$ After what time interval will the activity of the 90 $\mathrm{Sr}$ reach the agriculturally "safe" level of 2.00$\mu \mathrm{Ci} / \mathrm{m}^{2} ?$

Key Concepts

Unit Conversion

Unit conversion is the process of converting one set of units to another to maintain consistency in calculations. In contexts like radioactivity, converting between different units such as area (e.g., km² to m²) or radioactivity (e.g., curies to microcuries) is crucial for accurately determining concentration levels and understanding safety thresholds.

Activity

Activity is the measure of the rate at which a sample of radioactive material undergoes nuclear decay, typically expressed in units such as curies or becquerels. It reflects how many decay events occur per unit time and is directly proportional to the number of undecayed nuclei present in the sample.

Exponential Decay Law

Exponential decay is the mathematical model that describes the reduction in the number of undecayed nuclei as a function of time. This law is used to calculate the remaining quantity or activity of a radioactive substance at any given time and is governed by the decay constant or half-life of the substance.

Half-life

The half-life is the time required for half of the atoms in a radioactive sample to decay. It is a key parameter in nuclear physics that characterizes the rate of decay of a radioactive substance and allows for the calculation of remaining activity after a given time period.

Radioactive Decay

Radioactive decay refers to the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This principle is fundamental in understanding how the quantity of a radioactive substance decreases over time and is governed by statistical laws, leading to a predictable decay behavior described by an exponential function.

Decay Constant

The decay constant is a measure of the probability of decay of a single nucleus per unit time. It is mathematically related to the half-life, providing the necessary rate parameter in the exponential decay formula, and is essential for predicting how quickly a radioactive substance decays over time.

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