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A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 4 x 10-21 J apart. Use k = 1.4×10-23 J/K. Part 1 (a) When the nanoparticle's energy is in the range 5 x 4x 10-21 J to 6x4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i к Part 2 Submit Answer (b) When the nanoparticle's energy is in the range 8 x 4x 10-21 J to 9 x 4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i к Part 3 Submit Answer (c) When the nanoparticle's energy is in the range 5x4x 10-21 J to 9x 4x 10-21 J, what is the approximate heat capacity per atom? J/K Note that between parts (a) and (b) the average energy increased from "5.5 quanta" to "8.5 quanta". As a check, compare your result with the high temperature limit of 3k, where k 1.4 x 1023 J/K -

A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 4 x 10-21 J apart. Use k = 1.4×10-23 J/K. Part 1 (a) When the nanoparticle's energy is in the range 5 x 4x 10-21 J to 6x4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i к Part 2 Submit Answer (b) When the nanoparticle's energy is in the range 8 x 4x 10-21 J to 9 x 4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i к Part 3 Submit Answer (c) When the nanoparticle's energy is in the range 5x4x 10-21 J to 9x 4x 10-21 J, what is the approximate heat capacity per atom? J/K Note that between parts (a) and (b) the average energy increased from "5.5 quanta" to "8.5 quanta". As a check, compare your result with the high temperature limit of 3k, where k 1.4 x 1023 J/K -

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A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 4 x 10-21 J apart. Use k = 1.4 x 10-23 J/K. Part 1 (a) When the nanoparticle's energy is in the range 5 x 4x 10-21 J to 6 x 4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i K Part 2 Submit Answer (b) When the nanoparticle's energy is in the range 8 x 4x 10-21 J to 9 x 4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i K Part 3 Submit Answer (c) When the nanoparticle's energy is in the range 5 x 4x 10-21 J to 9 x 4x 10-21 J, what is the approximate heat capacity per atom? J/K Note that between parts (a) and (b) the average energy increased from "5.5 quanta" to "8.5 quanta". As a check, compare your result with the high temperature limit of 3k, where k = 1.4 x 10'23 J/K.
Transcribed Image Text:A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 4 x 10-21 J apart. Use k = 1.4 x 10-23 J/K. Part 1 (a) When the nanoparticle's energy is in the range 5 x 4x 10-21 J to 6 x 4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i K Part 2 Submit Answer (b) When the nanoparticle's energy is in the range 8 x 4x 10-21 J to 9 x 4x 10-21 J, what is the approximate temperature? (In order to keep precision for calculating the heat capacity, give the result to the nearest tenth of a degree.) i K Part 3 Submit Answer (c) When the nanoparticle's energy is in the range 5 x 4x 10-21 J to 9 x 4x 10-21 J, what is the approximate heat capacity per atom? J/K Note that between parts (a) and (b) the average energy increased from "5.5 quanta" to "8.5 quanta". As a check, compare your result with the high temperature limit of 3k, where k = 1.4 x 10'23 J/K.
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