When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of Np-240, a radioactive isotope of Neptunium, initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation.
A substance that has unstable nuclei is regarded as radioactive.
Alpha, beta, and gamma decay are three of the most prevalent types of decay, and they all entail the emission of one or more particles.

The formula so used: A = [tex]\frac{-dN}{dt}[/tex]

=> N = A ([tex]e^{-kt}[/tex]), where:

Now,

AS shown in the table (refer to the image attached), for k:

=> 322 = 1284[tex]e^{-2k}[/tex]

=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]

=> 0.25 = [tex]e^{-2k}[/tex]

Taking natural logarithm on both sides.

=> ln(0.25) = ln([tex]e^{-2k}[/tex])

=> ln(0.25) = (-2k) ln(e)

As ln (e) = 1,

=> ln (0.25) = -2k

=> -1.386 = -2k

=> k = 0.693

Now, for t = 1 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(1)}[/tex])

=> N = 1284 (0.5)

=> N = 642

For t = 3 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(3)}[/tex])

=> N = 1284 (0.125)

=> N = 160.6g

For t = 4 and k = 0.693, in the original formula, we get:

=> N = 1284 ([tex]e^{-0.693(4)}[/tex])

=> N = 1284(0.0625)

=> N = 80.3g

Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.

To learn more about radioactive decay, refer to the link: https://brainly.com/question/24195419

#SPJ4