A radioactive substance decays from 2.0kg to 1.6kg in 156 days.

How long would it take to decay to 1.1kg?

To answer this question, we need to determine the decay constant of the radioactive substance. The decay constant, denoted by λ, is a constant that characterizes the rate of decay of the substance. It can be determined using the following formula:

λ = (ln(N0/N))/(t)

Where:
N0 = initial mass of the substance
N = final mass of the substance
t = time taken for the substance to decay from N0 to N

In this case, the initial mass (N0) is 2.0kg, the final mass (N) is 1.6kg, and the time taken (t) is 156 days. Thus, we can substitute these values into the above formula to find the decay constant:

λ = (ln(2.0/1.6))/(156)

Using a scientific calculator, find the natural logarithm (ln) of (2.0/1.6), then divide the result by 156 to find the value of λ.

Once we have the value of the decay constant (λ), we can use it to determine the time (t1) it takes for the substance to decay to a mass (N1) of 1.1kg. Rearranging the formula, we have:

t1 = (ln(N0/N1))/(λ)

Substituting the values, we get:

t1 = (ln(2.0/1.1))/(λ)

Again, using a scientific calculator, find the natural logarithm (ln) of (2.0/1.1), then divide the result by λ to find the time for the substance to decay to 1.1kg.