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Uranium-238 possesses a half-life of approximately 4.5 billion years, a duration that underscores its stability and longevity in the natural environment. The concept of half-life refers to the time required for half of a given quantity of a radioactive substance to decay into its daughter isotopes. In the case of Uranium-238, this means that after 4.5 billion years, only half of the original amount of U-238 will remain, while the other half will have transformed into other elements through radioactive decay.
To determine the time it would take for a 2-gram sample of Uranium-238 to reduce to just 0.4 grams, one must first recognize that this represents a decay to 20% of the original mass. Given the half-life of U-238, the decay process can be calculated through successive halvings. After the first half-life, 1 gram of U-238 would remain, and after the second half-life, 0.5 grams would be present. Continuing this process, it becomes evident that reaching 0.4 grams will occur between the second and third half-lives, as 0.5 grams is the result of two half-lives.
In order to calculate the exact duration required to reach 0.4 grams from the initial 2 grams, one can apply the formula for exponential decay. This involves determining the number of half-lives needed to achieve the desired mass and then multiplying that number by the half-life duration of 4.5 billion years. The result will provide a precise estimate of the time required for the sample to decay to the specified amount of Uranium-238, illustrating the extensive timescales involved in the decay of this isotope.
