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.