Radioactive Decay

The decay of to involves the emission of both -particles and -particles. In the decay process: - Each -decay decreases the mass number by 4 and the atomic number by 2. - Each -decay increases the atomic number by 1, but the mass number remains unchanged. Since the decay process transforms to , we calculate the number of - and -decays required: - The mass number change: , so 8 -particles are emitted. - The atomic number change: , so 6 -particles are emitted. Thus, the correct number of - and -particles is 8 and 6, respectively.

The decay of radioactive materials can be described by the equation: Where: - is the remaining amount of the substance, - is the original amount, - is the decay constant, - is the time elapsed. For material A, it decays to 6.25 percent of its original amount. Therefore, the fraction remaining is , and we can express this decay process as: Taking the natural logarithm on both sides: For material B, it decays to 25% of its original amount. Therefore, the fraction remaining is , and we can express this decay process as: Taking the natural logarithm on both sides: Dividing the two equations gives: Simplifying this ratio: Thus, the ratio of the decay constants is .