Question

HNTV 8) Suppose v(y) = A Sin By, and y(y)=B Cos By are each solution to the particle in the box problem with the Hamiltonian, H = -(h/8x ma?)d/dy. Show that the linear combination (y) - A Sin By - B Cos By is also a solution and then determine the eigenvalue. (Hint: Hv=Ev). The Synthesis of 1,3,5,7,9,11,13-tetradecaheptaene conjugated compound with the formula H-[CH=CH]7-H produced a trace amount as reported by (Alexander Mebane, JACS 74 (20), page 5227-5229 (1952). The absorption maximum 2 max for this compound is 390 nm. It has a molar mass of 184.27 g/mol. Estimate the bond length of the conjugation compound. (Hint: Use the particle in one dimensional box model; Enn'h/8maf; and AE - hc/max)Draw the molecular energy level diagram for the pi-electrons and show the electronic transition that gives the max.

Answer 1

Answer & The linear combination will be an acceptable solution if it is an eigen function of H: • H(AsinBy – B Cosby) • H(Asingy) - H(B COSBY) (as His a linear :-( man) Casino 3) + (this may (8 casey) -- Camas de las esby] He was). (Bp.-simps] - Con ) (Apsinby) + () (-Bpcopy) very one (asmpy – Beospy) As hB is a constant therefore (Asinky-Brosby) is an eigen function of H. Hence (Asinky- Beosky) is an 87²ma? solution. acceptable ²6² 8R²maz Eigen value =