Orbitals s p d f Shapes - UNSOLVED PRACTICE SET

Q7. What is an atomic orbital? How does it differ from Bohr's concept of an orbit?

Q8. Describe the shapes of s and p orbitals. How many nodal surfaces does a 2p orbital have? 

Q9. What are the designations of the three p-orbitals? Why are they oriented perpendicular to each other?

Q10. Draw the shapes of the five d-orbitals. Which d-orbitals lie along the axes and which lie between the axes? 

Q11. Your art teacher asks you to draw a sphere, a dumbbell, and a cloverleaf. She then tells you that these shapes represent where electrons can be found around an atom's nucleus. Explain why an s-orbital is spherical and why a p-orbital is dumbbell-shaped, based on the mathematical solutions of the Schrödinger equation.

Q12. What is a radial node? How many radial nodes are present in a 3s orbital?

Q13. Explain the concept of atomic orbitals. Compare orbitals with Bohr's orbits. Describe the shapes of s, p, and d orbitals with neat diagrams. Explain what nodal surfaces are and why they occur.

Q14. Describe the quantum mechanical model's picture of electron distribution around the nucleus. Explain:

(a) Why the 1s orbital is spherical and has no nodes

(b) Why the 2p orbitals are dumbbell-shaped and have one nodal plane each

(c) Why the 3d orbitals have more complex shapes with two nodal planes

(d) How the shapes of orbitals influence chemical bonding

Why can we never pinpoint the exact location of an electron in an orbital?

Q15. During a 3D modelling activity in class, you are asked to construct models of different orbitals using balloons or clay.

(a) You inflate one balloon to represent a 1s orbital. Why is it perfectly spherical? What would happen if you tried to represent a 2s orbital with a slightly larger sphere?

(b) You use two elongated balloons joined at the centre to represent a p-orbital. Why must the three p-orbitals be perpendicular to each other?

(c) A classmate asks why d-orbitals have such complicated shapes. How would you explain that these shapes arise from the mathematical solutions for l = 2?

(d) Why are f-orbitals not discussed in detail at the Class 11 level, even though they exist for elements beyond atomic number 57?

Q16. The number of radial nodes in an orbital is given by (n − l − 1), and the number of angular nodes is given by l.

(a) Calculate the number of radial nodes and angular nodes for a 3p orbital.

(b) Calculate the total number of nodes for a 4d orbital.

(c) For a 2s orbital, verify that the number of nodes matches the formula. Draw a rough radial probability distribution curve showing the node.

(n = principal quantum number, l = azimuthal quantum number)

Q17. The maximum number of electrons in a subshell is given by 2(2l + 1), where l is the azimuthal quantum number.

(a) Calculate the maximum number of electrons in s, p, d, and f subshells.

(b) Verify that the total number of orbitals in a shell with principal quantum number n is n².

(c) If an atom has electrons filling up to the 3d subshell, what is the maximum number of electrons it can have? Show your calculation.

Q18. A student is studying the electron density distribution in different orbitals.

(a) For a 1s orbital, the electron density is maximum at the nucleus and decreases exponentially with distance. Sketch a graph of electron density vs. distance for 1s and 2s orbitals.

(b) For a 2p orbital, the electron density is zero at the nucleus and maximum at a certain distance. Why is there a nodal plane passing through the nucleus?

(c) The dₓᵧ orbital has electron density between the x and y axes, while the dₓ²₋ᵧ² orbital has density along the axes. How does this difference affect the way these orbitals participate in chemical bonding?