one fourthof the amount of radioactive element decays in 2490years . find outthe half life of this element

To determine the half-life of a radioactive element when you know that one-fourth of it decays in 2490 years, we can use the concept of half-lives. The half-life is the time it takes for half of a radioactive substance to decay. Let's break this down step by step.

Understanding the Decay Process

Radioactive decay follows a predictable pattern. When we say that one-fourth of the element has decayed, it means that three-fourths of the original amount remains. This can be expressed in terms of half-lives:

• After one half-life, half of the original amount remains.
• After two half-lives, half of the remaining half (which is one-fourth of the original amount) remains.

Calculating the Half-Life

Since we know that one-fourth of the element has decayed in 2490 years, we can deduce that this corresponds to two half-lives. Here’s how:

• Start with 100% of the radioactive element.
• After the first half-life, 50% remains.
• After the second half-life, 25% remains (which is one-fourth of the original amount).

Since two half-lives have passed in 2490 years, we can find the duration of one half-life by dividing the total time by the number of half-lives:

Mathematical Calculation

Let’s do the math:

Half-life = Total time / Number of half-lives

Half-life = 2490 years / 2 = 1245 years

Final Result

The half-life of the radioactive element is therefore 1245 years. This means that every 1245 years, half of the remaining radioactive material will decay, continuing the cycle until it is no longer detectable.

This concept is crucial in fields like nuclear physics, geology, and archaeology, where understanding the decay of elements helps in dating materials and understanding processes in nature.