Finding original amount in half-life problem

4,071

Since

$$\text{Amount remaining} =\text{Original Amount} \times \bigg(\frac{1}{2}\bigg)^{\text{number of half lives}} $$

solve for $X$ in the equation

$$10 = X \times \bigg(\frac{1}{2}\bigg)^{\frac{1000}{1590}}$$

Share:
4,071

Related videos on Youtube

jaykirby
Author by

jaykirby

Updated on August 01, 2022

Comments

  • jaykirby
    jaykirby over 1 year

    Say the half-life of an element is 1590 years. If 10g of the element is left after 1000 years, how much was there originally?

    • Gerry Myerson
      Gerry Myerson over 10 years
      What do you know about this kind of problem? Have you not been shown some formulas that might be useful?
    • jaykirby
      jaykirby over 10 years
      I know how to calculate half-life but don't know how to find the original amount.
    • Gerry Myerson
      Gerry Myerson over 10 years
      So, how do you calculate half-life?
    • jaykirby
      jaykirby over 10 years
      ln(fraction remaining) = -kt
    • Gerry Myerson
      Gerry Myerson over 10 years
      What does $k$ stand for? what does $t$ stand for? How would you use that formula? what would you have to know, and what computation would you do? Full sentences, please.
    • jaykirby
      jaykirby over 10 years
      k stands for rate constant and t for time. to use the formula you would need to know at least 2 of the 3 unknowns.
    • Angela Pretorius
      Angela Pretorius over 10 years
      The amount of the element has halved $\frac{1000}{1590}$ times. There was $\displaystyle 2^{\frac{1000}{1590}}\times 10g$ initially.