Half life

[phunkeyfantom]

Po (mass # 204, atomic # 84) undergoes radioactive decay with a half-life of 3.8 hours by emitting alpha particles. Two moles of pure Po (mass # 204, atomic # 84) are isolated and put on a scale. After 7.6 hours a reading of the sample's mass is made. Its mass is found to be.

I chose C. 400 grams but the correct answer is D. 402 grams. I'm confused as to how they came about obtaining the answer since the explanation offered wasn't that clear.

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[milski]

When you start you'll have 2 moles of Po or 408 g of material
After 3.8 hours, half of the Po will have decayed to something with mass #200 (one alpha particle is 2 protons/neutrons) and thus you'll have 204 g Po + 200 g something else.
Since only Po decays, after another 3.8 hours you'll have half of that Po - 102 g and 100 g of something else + the other 200 g of decayed product -> 402 g total mass

Alternatively, you know that two half periods later you'll have 1/4 of the initial compound, which means 1/2 mole Po and 3/2 mole of the decay product. 1/2 mole *204 g/mole + 3/2 mole *200 g/mole = 102 g + 300 g = 400 g

 

[phunkeyfantom]

When you start you'll have 2 moles of Po or 408 g of material
After 3.8 hours, half of the Po will have decayed to something with mass #200 (one alpha particle is 2 protons/neutrons) and thus you'll have 204 g Po + 200 g something else.
Since only Po decays, after another 3.8 hours you'll have half of that Po - 102 g and 100 g of something else + the other 200 g of decayed product -> 402 g total mass

Alternatively, you know that two half periods later you'll have 1/4 of the initial compound, which means 1/2 mole Po and 3/2 mole of the decay product. 1/2 mole *204 g/mole + 3/2 mole *200 g/mole = 102 g + 300 g = 400 g

Thanks so much. That makes sense.

 

[brianphu53]

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[milski]

Since only Po decays, after another 3.8 hours you'll have half of that Po - 102 g and 100 g of something else + the other 200 g of decayed product -> 402 g total mass


204/2 = 102 g. Shouldnt there be 102 grams of something else?

The decayed product has atomic mass of 200. An alpha particle is 2 protons and 2 neutrons, Po is 204, 204 - 2 - 2 = 200. After half of the Po has decayed, you have 1/2 mole Po and 1/2 mole decay product, so the total mass is 1/2*204+1/2*200=102+100=202.