sammy28

a + a = a 2a = a 2 = 1 2 + 2 = 2 4 = 2

Proof by contradiction. any number that isnt rational must be irrational, therefore start by making the contradiction that its rational: [math]\sqrt{2}=\frac{p}{q}[/math] where p, q are integers and q not equal to 0 with [math]\frac{p}{q}[/math] in lowest terms. [math]\frac{p^2}{q^2}=2[/math] so [math]p^2=2q^2[/math] so p is even. since p^2 is even, p must also be even (even x even = even) so you can write: [math]p=2m[/math] where m is an integer substituting this into the previous statement [math]4m^2=2q^2[/math] [math]2m^2=q^2[/math] So q^2 is even and so q must be even. But if both p and q are even then [math]\frac{p}{q}[/math] is not in lowest terms. Since there is a contradiction, the original assumption must be false. That is [math]\sqrt{2}[/mat] cannot be rational. therefore [math]\sqrt{2}[/math] is irrational

thanks for that. wiki seems to make a subtle distiction between uranianite and pitchblende it has on this page: http://en.wikipedia.org/wiki/Uranium_ore_deposits So if your not given a compound like U02 and UO3 which you can work back and get U4+ and U6+ how do you know what other ions of uranium there are? cheers sammy

Hi, A question in my chemistry 'O' level book says find out what Pitchblende is and where it comes from. I looked it up on wkipedia and it says its a compound of uranium and oxygen. U3O8 and U307 I tried to figure out whether a covalent bond could be made between the two but dont think it can unless you share the two electrons in the valence shell of uranium with the 6 in the oxygen. I thought covalent bonds had to be single, double, triplet, etc. Im I right in thinking that they will not covalently bond. im not sure how many electrons a U atom can loose being a transition element. If its a normal ion it would want to become U2+ which could balance with a O2- and become UO. Is this called Uranium (I) Oxide or Uranium (II) Oxide. We have been taught about Copper (I) and copper (II) where 1 electron is lost to make the octet and II where two electrons are lost Im not sure how this second one is stable. Can the number of stable ions be worked out or do you have to look them up? still not sure what the U3O8 and U307 bonds are. thanks for your help sammy