If you want to calculate the time it will take for a radioactive isotope to decay to a specific amount or to transform into a different isotope, you typically need to use the concept of the decay constant (λ) and the Bateman equation, which is a generalization of the decay equation for multiple radioactive species. The Bateman equation allows you to calculate the time it takes for a specific decay or transformation process to occur. Here's the Bateman equation for a single decay process:

N(t)=N0​⋅e^−λt

Where:

• N(t) is the amount of the original isotope remaining at time t.
• N0​ is the initial amount of the original isotope.
• λ is the decay constant for the specific decay process.
• t is the time.

To calculate the time it takes for the original isotope to decay into a different isotope or reach a specific activity level, you may need additional information about the specific decay process, such as the decay constant (λ) for that particular reaction.

Keep in mind that this equation is for a single decay process, and if you're dealing with a complex decay chain with multiple intermediate products, you would need to use a more elaborate version of the Bateman equation that accounts for all relevant decay processes in the chain.

In summary, to calculate the time it takes for a specific decay or transformation process to occur in a radioactive isotope, you would use the Bateman equation with the appropriate decay constant for that process.

If the above method is not satisfactorily effective, we can conclude that there isn't yet a single formula to calculate the entire lifespan of a radioisotope apart from the half-life, because the concept of half-life inherently describes the exponential decay of a radioactive substance.