A radioactive element has a half life of and 2500 years. In how many years will its mass decay by 90% of its initial mass?

A radioactive element has a half life of and 2500 years. In how many years will its mass decay by 90% of its initial mass?

Given a radioactive element with a half-life of 2500 years, we want to find the time it takes for its mass to decay by 90% of its initial mass.

To do this, we use the formula for exponential decay:

Final mass = Initial mass × (1/2)^{(t / T_1/2)}

Where:

• Final mass is the final mass of the element after decay,
• Initial mass is the initial mass of the element,
• t is the time in years, and
• T_1/2 is the half-life of the element in years.

Given that the final mass is 10% (or 0.1 times) of the initial mass, we can write:

0.1 × Initial mass = Initial mass × (1/2)^{(t / 2500)}

Solving for t:

t = 2500 × log₂(10)

Calculating the value, we find t ≈ 8305 years.

So, the mass of the radioactive element will decay by 90% of its initial mass in approximately 8305 years.

For more educational content, visit Nepali Educate.