Can you prove that n^5 - n is divisible by 5 for all n in ZZ
Feb 1, 2017 · See proof below Let the statement be P(n)=n^5-n P(1)=0, this is divisible by 5, the statement is true for n=1 P(k)=k^5-k=5m, where m in ZZ aassume that the statement is true for n=k Then, P(k+1)=(k+1)^5-(k+1) =k^5+5k^4+10k^3+10k^2+5k+cancel1-k-cancel1 =(k^2-k)+5(k^4+2k^3+2k^2+k) =5m+5(k^4+2k^3+2k^2+k) =5(m+(k^4+2k^3+2k^2+k)) Therefore, …
What are nonbonding molecular orbitals? + Example - Socratic
Apr 13, 2014 · A non-bonding orbital (NBMO) is a molecular orbital for which the addition or removal of an electron does not change the energy of the molecule. Molecular orbitals come from the linear combination of atomic orbitals. In a simple diatomic molecule such as HF, F has more electrons than H. The s orbital of H can overlap with the 2p_z orbital of fluorine to form a …
How can I calculate the bond order of benzene? | Socratic
Apr 11, 2014 · You draw the molecular orbitals. Then you add electrons and count the number of bonding and antibonding electrons. The bond order of a bond is half the difference between the number of bonding and antibonding electrons. BO = ½(B – A) The C-C σ Bonds Each C-C σ bond is a localized bond. It has 2 bonding electrons and 0 nonbonding electrons. σ BO = ½(B – A) = …
Using the MO diagram of #"NO"#, calculate the bond order
Aug 29, 2017 · The MO diagram for "NO" is as follows (Miessler et al., Answer Key): (The original was this; I added the orbital depictions and symmetry labels. For further discussion on the orbital energy ordering being "N"_2-like, see here and comments.) Quick overview of what the labels correspond to what MOs: 1a_1 is the sigma_(2s) bonding MO. 2a_1 is the sigma_(2s)^"*" …
What is the difference between bonding and antibonding
Aug 14, 2014 · Bonding orbitals place most of the electron density between the nuclei of the bonded atoms. Antibonding orbitals place most of the electron density outside the nuclei. > Electrons in bonding orbitals stabilize the molecule because they are between the nuclei. They also have lower energies because they are closer to the nuclei. Antibonding orbitals place less …
How do you find the taylor series for #ln(1+x^2)#? - Socratic
Jan 14, 2018 · We start by working out a taylor series for #ln(1+x)#.I will be expanding around #0#, so it will be a Maclaurin series.
Why is the energy ordering of the - Socratic
Sep 3, 2016 · The molecular orbitals of diatomic elements in the second period have orbital mixing effects, and from nitrogen to oxygen, the sigma_(2p_z) becomes lower in energy than the pi_(2p_x) and pi_(2p_y) orbitals since these effects have been decreasing across the period from left to right, and for nitrogen it is borderline. The relevant orbitals are the sigma_(g)(2s) (the …
Is 0 a rational, irrational, natural, whole, integer or real number?
Jun 28, 2015 · 0 is a rational, whole, integer and real number. Some definitions include it as a natural number and some don't (starting at 1 instead). Natural numbers are the ...