Explanation:
(a) potassium oxide with water
According to reaction,1 mole of potassium oxide reacts with 1 mole of water to give 1 mole of potassium hydroxide.
(b) diphosphorus trioxide with water
According to reaction,1 mole of diphosphorus trioxide reacts with 2 moles of water to give 2 moles of phosphorus acid.
(c) chromium(III) oxide with dilute hydrochloric acid,
According to reaction,1 mole of chromium(III) oxide reacts with 6 moles of hydrochloric acid to give 2 moles of chromium(III) chloride and 3 moles of water.
(d) selenium dioxide with aqueous potassium hydroxide
According to reaction,1 mole of selenium dioxide reacts with 2 moles of potassium hydroxide to give 1 mole of potassium selenite and 1 mole of water.
I was hoping that some choices would be given to choose from. As there are no choices given, so i am answering the question based on my knowledge and hope that it comes to your help. Calcium hydroxide is a good example of Arrhenius base. An Arrhenius base is actually a substance that releases a hydroxyl ion in water.
3.01 Ă— 10^24 Ă— (12/5) hydrogen atoms
Looking at the formula for the molecule, the ratio of carbon to hydrogen atoms is 5:12, so if we divide the number of carbon atoms by 5 and then multiply by 12, we can find the number of hydrogen atoms. Let's look at the available options and see what makes sense.
3.01 Ă— 10^24 Ă— (12/5) hydrogen atoms
* This is exactly correct.
(3.01 Ă— 10^24 / 5) hydrogen atoms
* Nope. This will tell you how many pentane MOLECULES you have, but not the number of hydrogen atoms.
3.01 Ă— 10^24 Ă— (5/12) hydrogen atoms
* Close, but the ratio (5/12) will tell you the number of carbon atoms you have if you give it the number of hydrogen atoms. So this choice is wrong.
3.01 Ă— 10^24 Ă— 12 hydrogen atoms description
* This would tell you the number of hydrogen atoms you have if you know the number of pentane molecules you have. So this choice is also wrong.
Answer to this is Radioactive isotopes.
Isotopes are the species of the same element having different atomic masses that means the number of protons remains the same but number of neutrons do differ. For example 
and 
are the two isotopes of Hydrogen (
).
Radioactive isotopes are the isotopes which release some kind of energy in the form of alpha particles, beta particles or gamma radiation. Examples of each of the decay processes are :
Alpha Decay: In this decay one alpha particle having atomic mass 4 and atomic number 2 or we can say a He molecule will come out. 
Beta Decay: In this decay a 
particle is emitted increasing the atomic number of the reactant by 1 unit.
Gamma Radiation: In this type of reaction only radiation is emitted out which does not change the original molecule.
