According to Quantum Mechanics, the translational energy levels e, of a single particle of mass m=...

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According to Quantum Mechanics, the translational energy levels e, of a single particle of mass m= 100 kg in a cubic box of volume V=L=1 cm are given by a) b) o) d) Tn with n = n+n+n and n,,,.n>0. 2ml Explain the fundamental role played by this model in statistical physics and show that the energy states of this particle can be conveniently represented in the so-called k-space such that =| -()*~* n. (6 marks) Use this model to establish a formula giving the number of states with energles less than or equal to ,. (6 marks) What is meant by density of states? Calculate the value of the density of states g(e) near e=0.025 eV and hence the number of energy states having an energy less than or equal to 0.025 eV. (6 marks) Show the effect of reducing the value of L to 1 nm. Calculate the value of L required to have &-&=1 eV. (7 marks) According to Quantum Mechanics, the translational energy levels e, of a single particle of mass m= 100 kg in a cubic box of volume V=L=1 cm are given by a) b) o) d) Tn with n = n+n+n and n,,,.n>0. 2ml Explain the fundamental role played by this model in statistical physics and show that the energy states of this particle can be conveniently represented in the so-called k-space such that =| -()*~* n. (6 marks) Use this model to establish a formula giving the number of states with energles less than or equal to ,. (6 marks) What is meant by density of states? Calculate the value of the density of states g(e) near e=0.025 eV and hence the number of energy states having an energy less than or equal to 0.025 eV. (6 marks) Show the effect of reducing the value of L to 1 nm. Calculate the value of L required to have &-&=1 eV. (7 marks)

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