Final answer:
To find out how much chromium-49 remains after 5 minutes from a 4-gram sample, you use the formula for exponential decay, considering the half-life of 42.3 minutes. However, the calculation is complex due to the short elapsed time relative to the half-life, and the exact answer would require more precise methods typically involving natural logarithms and the decay constant.
Step-by-step explanation:
The question involves the concept of the half-life of a radioactive element, in this case chromium-49. The half-life is the time taken for half of the radioactive atoms in a sample to decay.
For chromium-49, the half-life is approximately 42.3 minutes. If we start with a 4-gram sample and want to find out how much remains after only 5 minutes, which is a fraction of the half-life, we can use the formula for exponential decay:
N(t) = N0 × 0.5^(t/T)
Where:
- N(t) is the amount remaining after time t,
- N0 is the initial amount of the substance,
- T is the half-life of the substance, and
- t is the elapsed time.
However, since 5 minutes is a much shorter time than the half-life of 42.3 minutes, the amount of decay would be minimal. The formula is best suited for time periods that are comparable to or multiple of the half-life. The decay in this case is not straightforward to calculate without specialized equations or software, which typically involve natural logarithms and the decay constant.
As 5 minutes is about 1/8.46 of the half-life (42.3 minutes), we can estimate that a little less than 4 grams would remain after 5 minutes. However, without precise calculations, it's important to note that this is just an approximation.