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11 Dec 2019

Physical Chemistry: Ch 10 Introduction to quantum mechanics

How many interior nodes are there when the one-dimensional particle-in-a-box is in the state described by Î¨₅? by Î¨₁₀? by Î¨₁₀₀? Recall that âinterior nodesâ are all the nodes but those at the sides of the box.

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Physical Chemistry: Ch. 10 Introduction to Quantum Mechanics

What is the ratio of energy levels (E_A/E_B ) for a state having quantum numbers {n_x , n_y , n_z } in boxes with different dimensions â Box A being 1 nm Ã 1 nm Ã 1 nm and Box B being 2 nm Ã 2 nm Ã 2 nm? (b) Are the degeneracies of each set of quantum numbers the same for Box A and Box B? Explain your answer.

Answer:

(a) 4 10.82 â©xâª = (a/2), â© yâª = (b/2), â©zâª = (c/2)

Physcial Chemistry:Ch 10 Introduction to Quantum Mechanics

Carotenes are molecules with alternating CâC and C=C bonds in which the electrons are delocalized across the entire alternating bond system. As such, the electrons can be approximated as being a particle-in-a-box. Lycopene is a carotene found in tomatoes and watermelon. Assuming that the alternating carbon-carbon bond system is 2.64 nm wide:

(a) What is the energy of the n = 11 level?

(b) What is the energy of the n = 12 level?

(d) If, by the Bohr frequency condition, âE = hÎ½, what frequency and wavelength of light corresponds to the transition from n = 11 to n = 12?

Answer:

(a) 1.05Ã10^â18 J (b) 1.24Ã10^â18 J (c) 1.9Ã10^â19 J (d) Î½ = 2.87Ã10¹⁴ s ^â1 , Î» = 1.05 Âµm

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Physical Chemistry: Ch 10 Introduction to quantum mechanics

How many interior nodes are there when the one-dimensional particle-in-a-box is in the state described by Î¨₅? by Î¨₁₀? by Î¨₁₀₀? Recall that âinterior nodesâ are all the nodes but those at the sides of the box.

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Physical Chemistry: Ch 10 Introduction to quantum mechanics How many interior nodes are there when the one-dimensional particle-in-a-box is in the state described by Î¨5? by Î¨10? by Î¨100? Recall that âinterior nodesâ are all the nodes but those at the sides of the box.

Related textbook solutions

Basic Chemistry

Principles of Chemistry Molecular Approach

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Physical Chemistry: Ch 10 Introduction to quantum mechanics

How many interior nodes are there when the one-dimensional particle-in-a-box is in the state described by Î¨₅? by Î¨₁₀? by Î¨₁₀₀? Recall that âinterior nodesâ are all the nodes but those at the sides of the box.