One-eighth of a sample of 227 Th 90 (227 90 Th) remains undecayed after 54 days. What is the half-life of the thorium isotope?

Half-Life = 18 days

Explanation:

Isotope decay follows the equation:

Ln[A] = -kt + ln[A]₀

Where [A] is amount of isotope after time t,

k is rate constant

[A]₀ is initial amount of isotope.

If we solve rate constant, we can find half-life by using:

Half-life = ln 2 / Rate constant

Replacing in isotope decay equation:

Ln[1/8] = -k*54 days + ln[1]

-2.07944 = -54k

0.0385days⁻¹ = k

Half-Life = ln 2 / 0.0385days⁻¹

answer : one can design an experiment using a liquid and an additive that can be added to the liquid and observe the chemical changes in the reaction species.

one would need a beaker which is filled with a known amount of the liquid in which thermometer is placed to measure the temperature changes; after addition of the additive to the liquid solution one can note down the temperature change and find whether the reaction is endothermic or exothermic in nature. by subtracting the initial temperature value with the final temperature one can find the temperature changes.

various combinations of liquid and additive can be used. liquid in this case can be a known quantity of water and additives can be epsom salt or without epsom salt the experiment can be conducted to notice the changes. water and ice, hydrogen peroxide and dry yeast, vinegar and baking soda,etc.

answer seismograph;