problem 9.50 Calculate the first three energy levels, in kJ mol-1, for an electr

Question

problem 9.50

Calculate the first three energy levels, in kJ mol-1, for an electron in a potential well 0.5 nm in width infinitely high potential outside. For a particle in a cubical box calculate E(8ma2/h2) for the first 10 states. What is the degeneracy for each energy level? Assume the form for the ground-state wavefunction of the harmonic oscillator, and substitute this into the Schrödinger equation. Find the value of a that makes this an eigenfunction. figure 9.6 shows that the quantum mechanical harmonic oscillator can be in regions forbidden to a classical harmonic oscillator, (a) Find an integral expression for the probability that the particle will be in the classically forbidden region for the ground state, (b) Using tables for Gauss,an

Explanation / Answer

Ans. Energy in nth level for 1 dimensional particle = n2h2/8mel2,
where n is the energy level, h - planck's constant, me- mass of electron, l - 0.5 nm

Therefore energy in 1st level per mol = (h2/8mel2)*6.02*10^23 = 145 kcal/mol

Energy in 2nd level per mol = 4*(h2/8mel2)*6.02*10^23 = 580 kcal/mol

Energy in 3rd level per mol = 9*(h2/8mel2)*6.02*10^23 = 1305 kcal/mol

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