the half-life of cobalt-60 is 5.20 years.. how many milligrams of a 2.000-mg sample remains after 6.55 years

To find the amount of cobalt-60 remaining after 6.55 years, we can use the formula:

Amount remaining = Initial amount × (1/2)^(t / half-life)

Where:
- Initial amount is the starting amount, which is 2.000 mg.
- t is the time elapsed, which is 6.55 years.
- Half-life is the time it takes for half of the substance to decay, which is 5.20 years.

Plugging in the values:

Amount remaining = 2.000 mg × (1/2)^(6.55 / 5.20)

Calculating the values:

Amount remaining = 2.000 mg × (0.5)^(1.2596153846153846)

Amount remaining = 2.000 mg × 0.7937

Amount remaining ≈ 1.5874 mg

Therefore, approximately 1.5874 milligrams of the cobalt-60 sample will remain after 6.55 years.

To calculate the amount of cobalt-60 remaining after 6.55 years, we can use the formula:

Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)

In this case, the initial amount is 2.000 mg, the time elapsed is 6.55 years, and the half-life is 5.20 years.

Let's substitute these values into the formula:

Amount remaining = 2.000 mg * (1/2)^(6.55 years / 5.20 years)

First, let's calculate the exponent:

Exponent = 6.55 years / 5.20 years = 1.2596

Next, let's calculate (1/2)^1.2596:

(1/2)^1.2596 ≈ 0.7861

Now, let's calculate the amount remaining:

Amount remaining = 2.000 mg * 0.7861 ≈ 1.5722 mg

Therefore, approximately 1.5722 milligrams of the original 2.000-milligram sample of cobalt-60 remains after 6.55 years.

k = 0.693/t1/2

ln(No/N) = kt
No = 2.000 mg
N calculate
k from above
t 6.55 years.