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Working with schrodinger atomic model - Quantum states

Please see the attached file.

According to the Schrodinger atomic model, each quantum state of an atom or ion can be labelled using two quantum numbers n and l.

Write down a formula for the energy of each of the quantum states of the hydrogen like boron ion B4+.

For a given value of n, state how the number of quantum states depends on the value of the second quantum number l.

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According to the Schrodinger atomic model, each quantum state of an atom or ion can be labelled using two quantum numbers n and l.

Write down a formula for the energy of each of the quantum states of the hydrogen like boron ion B4+.

For a given value of n, state how the number of quantum states depends on the value of the second quantum number l.

I have sent a detailed explanation on the last posting by you to the BM admin. I am adding it here also.

Let us consider the case of an ion with the charge of nucleus being Ze and an electron moving with a constant speed v along a circle of radius r with the center at the nucleus. The force acting on the electron is that due to Coulomb attraction and is equal to
F = Ze2/40r2
The acceleration of the electron is towards the center and has a magnitude v2/r. If m is the mass of the electron, from Newton's law we obtain
Ze2/40r2 = mv2/r
Using Bohr's angular momentum quantization rule for the value n, the Principal quantum number, we obtain both the velocity v, and the radius r as:
v = Ze2/20hn r = 0h2n2/ mZe2 ...(i)
We see that the ...

Solution Summary

The solution provides and easy to follow explanation of the concepts and gives all mathematical steps wherever necessary.

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