A radioactive element with a half-life of 1,000 years, and starting mass of 20 grams, will need 2,000 years to decrease to 5 grams.
Explanation:
The radioactive elements all have a specific half-life. Each element's half-life is well known, and they are used by scientists of numerous fields as they are excellent for determining the age of a particular item, be it or organic or non-organic nature. In this case, we have a radioactive element with a half-life of 1,000 years, and starting mass of 20 grams.
The half-life basically means that half of the mass of an element is lost during a particular period of time. For the element in question we need to find out how much time will be needed for it to decrease to 5 grams. In order to get to the result, we just need to add 1,000 years on every decrease of half of the mass:
20/2 = 10
10/2 = 5
So in 1,000 years, the element in question will decrease to 10 grams, and in further 1,000 years (2,000 cumulatively) it will decrease to 5 grams.
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Eₖ = √1/2 mv²
Eₖ/v² = 1/2 m
2Eₖ/v² = m
mgh = 1/2 mv²
gh = 1/2 v²
2gh = v²
v = √2gh
= √2 × 10 N/kg × 2 m
= 6.324 ms⁻¹
m = 9.8/(6424)²
= 9.8/39.993
= 0.245 g
I am not sure if it's correct.
i transposed for m in the first equation then to find the velocity I combined the potential and kinetic energy equation. there was no mass because velocity doesn't depend on the mass
Then I used earth's gravitational field strength (g) 10 N/kg and the 2 m was the height provided in the question
you can try working and see if you get the same
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Explanation:
