I need help with high school chemistry (4 m.c.)?

Question

I need help with the following multiple choice questions, your help is greatly appreciated.

After 32 days, 5 milligrams of an 80-milligram sample of a radioactive isotope remains unchanged. What is the half-life of this element?

1) 8 days
2) 2 days
3) 16 days
4) 4 days

What is the total mass of 222Rn remaining in an original 160-milligram sample of 222Rn after 19.1 days?

1) 2.5 mg
2) 5.0 mg
3) 10. mg
4) 20. mg

Which element forms an ion that is larger than its atom?

1) aluminum
2) chlorine
3) magnesium
4) sodium

Which element is so active chemically that it occurs naturally only in compounds?

1) potassium
2) silver
3) copper
4) sulfur

Answer 1

First question:
One half-life leaves 40 mg, two leaves 20 mg, three leaves 10 mg, and four leaves 5 mg. So the half-life is 32 divided by 4, which is 8. So the answer is 8 days (1).

Second question:
The half-life of 222Rn is 3.825 days, so 19.1 is five times its half-life. So there will be 160/(2^5) mg left, so the answer is 5 mg (2).

Third question:
Aluminum, magnesisum, and sodium all form positive ions, which means that they lose electrons, so they get smaller. Chlorine forms a negative ion, so it gains an electron and hence gets bigger. So the answer is chlorine (2).

Fourth question:
Potassium, and all the elements in that column of the periodic table are highly reactive. Silver and copper are both common metals that you might see in jewlrey and coins, and are mined from certain rocks, where it is found naturally in small pockets. Sulfur occurs naturally around volcanos. So the answer is potassium (1).

Answer 2

And the answers are:
8 days
5 grams (5 half lives have passed each half life is 3.82 days)
chlorine (as the chloride ion is larger than the atom)
Potassium is very active and not free in nature.

Answer 3

8 days
nt enough info, I do not have half life of Rn222
Cl
K