Legend has it that, many centuries ago, archimedes jumped out of his bathtub and ran across town nakedscreaming "eureka! " after he solved an especially difficultproblem. though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinkingcontains some water molecules that were in archimedes' bathwaterthat day, because water doesn't get created or destroyed on a largescale. it follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. in themore than two thousand years since his discovery, the watermolecules from archimedes' bathwater have been through this cycleenough times that they are probably about evenly distributedthroughout all the water on the earth. when you buy a can of soda, about how many molecules from that famous bathtub of archimedes arethere in that can?

8652.36857143 x molecules

Explanation:

We need a lot of assumptions in this case.

1. We don't know the mass of water that was present in Archimedes' bath tub that day.

2. Since it recycles, we don't know the total mass of water present on earth.

Assuming the total mass of water on earth is 1.4 × tonnes;

converting tonnes to kgs -->>  1.4 × kg

Since only 2.5% of this is fresh, (the rest is saline and ocean-based)

-->> 2.5% of 1.4 × kg = 0.035  × kg

An average bath tub holds about 80 gallons of water.

80 gallons to kgs = 302.8329 kg

Using Avogadro's number,

we have about 6 × molecules in 18g of water;

1kg of water would contain about 3.3 × molecules.

An average water can holds about 355mL of fluid.

Therefore the number of molecules in the can is .

The number of bathtub molecules present in the can is;

302.8329 x / 0.035 x

= 8652.36857143 x molecules

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

beta is electron from nucleus

something from nucleus has changed, but charge must be same for cons of charge