What is an orbital? Explain the point and boundary surface diagram of orbitals.

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(N/A) Orbital: The region in space around the nucleus where the probability of finding an electron is maximum is called an orbital. In each orbital,there is a region where the probability of finding an electron is approximately $90 \%$. For this,$|\Psi|^{2}$ is small,but it gives a definite value for a specific distance from the nucleus. It is not possible to draw any geometrical figure that encloses a region of $100 \%$ probability. Therefore,we draw the figure for $90 \%$ probability of finding an electron.
Point and boundary surface diagram of orbitals: In a point diagram,dots are used to represent the probability density. By clustering these points,the shape of the orbital is visualized. In a boundary surface diagram,a surface is drawn for an orbital within which the value of the probability density $|\Psi|^{2}$ is constant.
Example: The boundary surface diagrams of $1s, 2s, 2p_{x}, 2p_{y}, 2p_{z}$ orbitals are standard representations.

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The electronic configuration together with the quantum numbers of the last electron for lithium $(Li)$ is:

The arrangement of orbitals on the basis of energy is based upon their $(n + l)$ value. Lower the value of $(n + l)$,lower is the energy. For orbitals having same values of $(n + l)$,the orbital with lower value of $n$ will have lower energy.
$(I)$ Based upon the above information,arrange the following orbitals in the increasing order of energy.
$(a)$ $1s, 2s, 3s, 2p$
$(b)$ $4s, 3s, 3p, 4d$
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$(d)$ $5f, 6d, 7s, 7p$
$(II)$ Based upon the above information,solve the questions given below:
$(a)$ Which of the following orbitals has the lowest energy? $4d, 4f, 5s, 5p$
$(b)$ Which of the following orbitals has the highest energy? $5p, 5d, 5f, 6s, 6p$

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Which of the following sets of quantum numbers is correctly matched?

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