Concept explainers
To rank:
The electrons according to their ground state energies
Answer to Problem 1Q
Solution:
The ranking of electrons according to their ground state energies is
Explanation of Solution
1) Concept:
Using the formula for ground state energy of an electron in one dimensional infinite potential well, we can find the relation between energy and width of the well, and then from the given values of widths, we can rank the electrons according to their ground state energies.
2) Formulae:
3) Given:
i)
ii)
iii)
4) Calculations:
The ground state energy of an electron in one dimensional infinite potential well is given by
From this, we can interpret that
Since,
Then,
Conclusion:
The energy of an electron in one dimensional infinite potential well increases with the decreasing length of the potential well.
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