The half-life of a radioactive element is 10 hours. The fraction of initial radioactivity of the element that will remain after 40 hours is

Explanation

Beta (β), also known as the current gain, is a dimensionless quantity that represents the ratio of the collector current (Ic) to the base current (IB) in a bipolar junction transistor (BJT). Mathematically, β = Ic / IB.Since α (alpha) represents the common-base current gain (Ic / IE) and β (beta) represents the common-emitter current gain (Ic / IB), we can use the relationship between them:β = α / (1 - α)We are given that α varies between 20/21 and 100/101. Let's find the minimum and maximum values of β within this range:Minimum β:Minimum α = 20/21β = (20/21) / (1 - 20/21)β ≈ 0.952Maximum β:Maximum α = 100/101β = (100/101) / (1 - 100/101)β ≈ 0.990Therefore, based on the provided information, the value of β lies between 0.952 and 0.990, which is closer to option b than the other options. However, it's important to note that this is an approximation due to the limited range of α values given.