Question

nobelium-259 is a radioactive substance that decays according to the following function, where is the initial amount present, and is the amount present at time (in minutes). find the half-life of nobelium-259. do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

The half-life of nobelium-259 can be calculated by solving for the number of half-lives it takes for the initial amount to decay to half that amount.

Step-by-step explanation:

The half-life of a radioactive substance is the time it takes for half of the substance to decay. In the case of nobelium-259, we have the initial amount present as 'No' and the amount present at time 'N1'. The equation for the amount remaining after 'n' half-lives is given by:

N1 = No * (1/2)^n

Using this equation, we can solve for the number of half-lives it takes for nobelium-259 to decay from its initial amount to half that amount. Let's denote this time as 't'. We know that N1/No = 1/2, so:

1/2 = (1/2)^t

To solve for 't', we can take the logarithm of both sides of the equation:

log(1/2) = t * log(1/2)

t = log(1/2) / log(1/2)

Using a calculator, we find that t is approximately 1.

Answer 2

The half-life of a radioactive substance is calculated by setting the amount of substance left after time t, to half the original amount and solving for t using the decay function specific to that substance.

Step-by-step explanation:

The question being asked is how to find the half-life of nobelium-259, a radioactive substance. The half-life is the amount of time it takes for half of the radioactive nuclei in a substance to decay. To calculate the half-life, we use the decay function provided for the substance, which represents how the quantity of the substance decreases over time. The formula for the amount remaining after n half-lives is given by the amount of substance left, N, equals the initial amount of substance, No, divided by 2 raised to the power of n (N = No / (2n)). Assuming we know the decay function for nobelium-259 (which could be derived from a first-order decay rate equation), we can set N equal to No / 2 to find the half-life by solving for t, the time elapsed.