The electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using n?h? En 8ml?n = 1, 2, 3, .. where L is the length of the 1D chain. Assuming L = ao(N – 1), where N is the number of Na atoms and ao = 0.360 nm is the internuclear distance. a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enough b) Thermal energy at room temperature is 4.15 × 10-21 J. Calculate the minimum number of Na atoms required so that the energy gap is smaller than the thermal energy,

The electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using n?h? En 8ml?n = 1, 2, 3, .. where L is the length of the 1D chain. Assuming L = ao(N – 1), where N is the number of Na atoms and ao = 0.360 nm is the internuclear distance. a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enough b) Thermal energy at room temperature is 4.15 × 10-21 J. Calculate the minimum number of Na atoms required so that the energy gap is smaller than the thermal energy,

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

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Question

The electronic structure of one-dimensional chain of sodium (Na) atoms can be
approximately described by the particle-in-a-box model. The energy of each state can
be calculated using
n?h?
En
8mlz п 3 1,2, 3, ...
where L is the length of the 1D chain. Assuming L = ao(N – 1), where N is the
number of Na atoms and ao = 0.360 nm is the internuclear distance.
a) Determine the energy gap between the highest occupied energy level and the
lowest unoccupied energy level as a function of N. Assume that N is an even number
that is large enough
b) Thermal energy at room temperature is 4.15 × 10-21 J. Calculate the minimum
number of Na atoms required so that the energy gap is smaller than the thermal
energy.

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