The particle-on-a-ring is a useful model for the motion of electrons around a co

Question

The particle-on-a-ring is a useful model for the motion of electrons around a conjugated macrocycle such as octatetrene, for example. Treat the molecule as a circular ring of radius 0.460 nm, with 10 electrons in the conjugated system moving along the perimeter of the ring. Assume based on the Pauli Exclusion Principle that in the ground state of the molecule each state is occupied by two electrons with opposite spins.
(a) Calculate the energy of an electron in the highest occupied level in joules.
J
(b) Calculate the (absolute magnitude of the) angular momentum of an electron in the highest occupied level in J-s.
J-s
(c) Calculate the frequency of radiation in Hz that can induce a transition between the highest occupied and lowest unoccupied levels.
Hz

Explanation / Answer

as we know dat

Energy = {Mi^2 * h^2}/2I

where I is moment of inertia

since there is total 10 electrons

dat means highest occupied state Mi = +-2

lz = +-(2*1.055*10^-34)= 2.11*10^-34 Js

I = mr^2

= 9.11*10^-31 * 460 * 10^-12 = 1.93*10^-49kgm^2

hence energy = 4 * (1.055*10^-34)^2/2*1.93*10^-49

= 1.1533 * 10^-19 J

b. lowest occupied energy = 9 * (1.055*10^-34)^2/2*1.93*10^-49

= 2.60 * 10^-19 J

Hence frequency = delta E/h

= (2.60-1.153)*10^-19/6.6*10^-34

= 2.19 * 10^14 Hz

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.