Why do you need the formula x=2n2squared to figure out the energy level?

Question

For the electron cloud? What is the purpose and how is it solved?

What does 1,2,3,4 mean? The 1st shell 2nd shell? Does the first one which can only allow 2 count as a shell? And what do the atomic mass and atomic number have to do with each other?

And lithium has an atomic mass of 3 and an atomic number of 6.941. What is the .941 about? Is it an unfilled electron?

Anyone please?

Answer 1

I'm afraid that you are very badly confused. Let's handle each statement in order:

"Why do you need the formula x=2n2squared to figure out the energy level?"

I'm not even sure what you're trying to say here - I'm guessing that you mean x=2n² - and the answer is that you don't need it to figure out the energy level for the electron cloud - the correct formula for the energy of an electron is (tbltr)A²/n², where Q is the atomic number, n is the principal quantum number of the electron shell, and tbltr is the product of -1, Planck's constant, the speed of light, and Rydberg's constant. I abbreviate it as tbltr because it's too buggering long to remember. What x=2n² gives you is the number of electrons that can be held in a the nth electron shell. This can easily be verified by noting that electrons in shell n must have an azimuthal quantum number in the range 0 to n-1 and for each azimuthal quantum number, it can take on values for the magnetic quantum number between L and -L. There are obviously 2L+1 such numbers (L negative, 0, and L positive), thus the number of orbitals in the shell is (i=0, n-1)∑(2i+1) which is 1+ (i=1, n-1)∑(2i+1) ⇒ 1+ 2(i=1, n-1)∑i + (i=1, n-1)∑1 ⇒ 1+ 2(n)(n-1)/2 + n - 1 ⇒1+n²-n+n-1 ⇒n². However, you may place up to two electrons in each orbital (one with spin up, the other with spin down), thus the number of electrons in the nth orbital is 2n².

Actually, I doubt you remembered all that, but you will need it in chemistry, which is why I went over it.

"What does 1,2,3,4 mean? The 1st shell 2nd shell?"

When writing out electron structure, the integer on the left of each term refers to the principal quantum number, which is indeed the number of the shell.

"Does the first one which can only allow 2 count as a shell?"

Yes, absolutely. I am not rightly able to understand the sort of confusion that would provoke such a question.

"And what do the atomic mass and atomic number have to do with each other?"

Nothing.

Well, not quite nothing, but there's not a linear relationship between them. The atomic mass is just what it sounds like - the mass of the atom, in amus (amu stands for atomic mass unit and is defined as exactly 1/12 the mass of a carbon-12 atom). The atomic number is the number of protons in an atom - it is this number, and this number alone, which determines the type of element you're dealing with - all atoms with 13 protons are aluminum atoms and in fact aluminum is just a (in)convenient way of saying "atoms with 13 protons." Now, the main factors in determining the mass of the atom are the numbers of protons and neutrons in an atom - electrons are less than 1/1000 of the mass of a proton and carry too little mass to make any significant difference. It so happens that protons and neutrons are about the same mass and so the atomic mass will be approximately the atomic number plus the number of neutrons. Now, atoms with more protons usually require more neutrons to hold the nucleus together, and so the sum of protons+neutrons is usually higher for higher numbered atoms, and so atoms with higher atomic number are usually more massive. Not always though - the most stable isotope of plutonium (atomic number 94) has an atomic mass of about 244, while the most stable isotope of americium (atomic number 95) has an atomic mass of only 243.

"And lithium has an atomic mass of 3 and an atomic number of 6.941."

No, Li has an atomic _number_ of three and an atomic _mass_ of 6.941. Do not confuse the two.

"What is the .941 about? Is it an unfilled electron?"

Absolutely not. First of all electrons have only a negligible effect on the mass of an atom. Second, measurements of atomic mass usually only measure the nucleus anyway. The reason for the fractional values of atomic mass are threefold:

#1: Most elements have more than one stable isotope. Because different isotopes of the same element are not distinguishable chemically, a pure sample of an element, however obtained, will contain a mixture of different isotopes. While chemists could, in principle, simply publish the exact masses of each isotope and then account for the relative abundances in their calculations, most of the time chemists don't care about the individual isotopes and just want to find out how many moles of an element they have, and as such going through the calculation would represent a whole lot of unnecessary work. In order to avoid this, the atomic masses published are averages of the masses of all the different isotopes in nature, weighted by their relative abundance. This weighting means that even if each isotope had an integer mass, the published value for the element's mass would not.

#2: In point of fact though, even a single isotope of an element will rarely have an integer mass (exception: carbon-12), for two reasons. First, the mass of the neutron is not equal to the mass of the proton - the neutron is slightly heavier, and so if a proton weighed exactly 1 amu (it doesn't, as I shall explain in a moment), then a neutron would not have an integral value for its mass and the sum of the masses of the protons and neutrons in the atom would not be an exact integer value.

#3: The final reason that the masses are fractional is because the mass of an atomic nucleus is not the sum of the masses of its constituent protons and neutrons. Each nucleon (a nucleon is simply a proton or neutron) is very tightly bound in the nucleus and would require a lot of energy to break free from it. By conservation of energy then, each nucleon has a significant amount of negative potential energy. You will recall that E=mc² - the reduction in energy that protons and neutrons get from being bound in the nucleus is in fact so great that it shows up as a measurable reduction in mass. Because different atoms have different binding energies, this means that their masses will differ by more than the masses of their constituent nucleons. To wit: if a U-235 nucleus is struck by a neutron, it might decompose into Kr-92 and Ba-141 plus three free neutrons. There are the same number of protons (92) and neutrons (144) as in the original uranium nucleus (plus the neutron that hit it), but the mass has been reduced, because the nucleons the krypton and barium are more tightly bound than the nucleons in the uranium. Excess energy is also released to the environment in this reaction.

Note that strictly speaking, chemical bonds also change the mass of the atom. The difference between them and nuclear bonds is that the nuclear bonds cause big enough changes to be measured, whereas chemical bonds do not.

Answer 2

to find out the maximum number of electrons that can be accommodated in a given energy level.by substituting 1,2,3,4 for n we van find the max no of electrons in level 1,level 2 etc

Answer 3

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