For what value of the principal quantum number n would the effective radius, as shown in a probability density dot plot for the hydrogen atom, be 1.00 mm? Assume that has its maximum value of n-1. (Hint:See Fig.39-24.)
The value of principal quantum number is .
The given data is listed below as,
The principal quantum number is used to describe the electron’s state and is the one four quantum number assigned to each electron in an atom.
The value of the principal quantum number is natural number.
According to the fig. 39-24. the principal quantum number satisfies,
Here, the Bohr radius is .
Solving the above equation will give the value of the principal quantum number is,
Substitute for r in the above equation.
Hence, the value of principal quantum number is .
If you double the width of a one-dimensional infinite potential well, (a) is the energy of the ground state of the trapped electron multiplied by or some other number? (b) Are the energies of the higher energy states multiplied by this factor or by some other factor, depending on their quantum number?
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