(a)
The lowest energy of the system in which electrons occupy respective state.
(a)
Answer to Problem 17P
The lowest energy of the system in which electrons occupy respective state is
Explanation of Solution
The particle placed in a cubical box is a well-known model in the field of
The particle in a box is a completely hypothetical model which illustrates the basic difference between the classical and quantum models. According to
Write the expression for the energy of the particle in cubical box.
Here,
According to Pauli Exclusion Principle, no more than two fermions can occupy same state. The electros are also fermions and are identical due to which any two electrons can occupy any state.
The electrons will, first, occupy ground state and then they will occupy further states with two electrons filled in each state.
The minimum energy of the system is the sum of energies of electrons present in ground state and other states. The electrons can also occupy the degenerate energy state due to which there can be three possible combinations, of respective
The energy of the electrons presents in the states
Write the expression for the minimum energy of the system of 8 electrons.
Simplify the above expression.
Here,
Conclusion:
Substitute
Substitute
Substitute
Thus, the lowest energy of the system in which electrons occupy respective state is
(b)
The lowest energy of the system of particles which have same mass as electrons but do not obey exclusion principle.
(b)
Answer to Problem 17P
The lowest energy of the system of particles which have same mass as electrons but do not obey exclusion principle is
Explanation of Solution
Since, the particles do not obey exclusion principle. Therefore all the particles can occupy same state that is ground state.
Write the expression for the minimum energy.
Here,
Conclusion:
Substitute
Substitute
Thus, the lowest energy of the system of particles which have same mass as electrons but do not obey exclusion principle is
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Chapter 9 Solutions
Modern Physics
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