Orbital Diagrams

Q.

The wave function, ${\Psi }_{n,l,m_l}$ is a methematical function whose value depends upon spherical polar coordinates (r, θ, Ф) of the electron and characterized by the quantum numbers n, l and m. Here r is distance from nucleus, θ is colatitude and Ф is azimuth. In the mathematical functions given in the Table, Z is atomic number and $a_0$ is Bohr radius.

Column 1	Column 2	Column 3
(i) 1s orbital	(i) ${\Psi }_{n,l,m_l}\propto {\left(\frac{Z}{a_0}\right)}^{\frac{3}{2}}{e}^{\left(\frac{-Zr}{a_0}\right)}$	(P)
(ii) 2s orbital	(ii) One radial node	(Q) Probability density at nucleus $\propto \frac{1}{a_0^3}$
(iii) 2 $p_z$ orbital	(iii) ${\Psi }_{n,l,m_l}\propto {\left(\frac{Z}{a_0}\right)}^{\frac{5}{2}}r{e}^{\left(\frac{-Zr}{2a_0}\right)}cos\theta$	(R) Probability density is maximum at nucleus
(iv) 3 $d_z^2$ orbital	(iv) xy-plane is a nodal plane	(S) Energy needed to excite electron from n = 2 state to n = 4 state is$\frac{27}{32}$ times the energy needed to excite electron from n = 2 state to n = 6 state

For $H{e}^{+}$ion, the only INCORRECT combination is:

1. (l) (i) (P)
2. (l) (iv) (R)
3. (ll) (i) (Q)
4. (l) (i) (S)

Q. If $0.53\stackrel{\circ }{A}$ is the Bohr's radius for the $1^{st}$ orbit of hydrogen atom, the correct statement (s) among the following is/are :

1. The product of ${\Psi }^2$ and $4\pi r^2$ increases till it reaches at the distance of $0.53\stackrel{\circ }{A}$
2. ${\Psi }^2$ goes on increasing till it reaches at the distance of $0.53\stackrel{\circ }{A}$
3. $\Psi$ goes on increasing till it reaches at the distance of $0.53\stackrel{\circ }{A}$
4. The nodal point for the 1s orbital is at $0.53\stackrel{\circ }{A}$

Q. Match the List - I with List - II and select the correct set from the following sets given below:
$\begin{array}{cccc}& \text{List - I}& & \text{List - II}\\ \text{(A)}& \text{The number of subshells in an}& \text{(1)}& n^2\\ & \text{energy level}& & \\ \text{(B)}& \text{The number orbitals in a}& \text{(2)}& 3d\\ & \text{shell}& & \\ \text{(C)}& \text{The number of orbitals in a subshell}& \text{(3)}& 2l+1\\ \text{(D)}& n=3,l=2& \text{(4)}& n\end{array}$

1. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(a)}& 4& 1& 3& 2\end{array}$
2. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(b)}& 3& 1& 4& 2\end{array}$
3. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(c)}& 1& 4& 3& 2\end{array}$
4. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(d)}& 3& 4& 1& 2\end{array}$

Q. Match the List - I with List - II and select the correct set from the following sets given below:
$\begin{array}{cccc}& \text{List - I}& & \text{List - II}\\ \text{(A)}& \text{The number of subshells in an}& \text{(1)}& n^2\\ & \text{energy level}& & \\ \text{(B)}& \text{The number orbitals in a}& \text{(2)}& 3d\\ & \text{shell}& & \\ \text{(C)}& \text{The number of orbitals in a subshell}& \text{(3)}& 2l+1\\ \text{(D)}& n=3,l=2& \text{(4)}& n\end{array}$

1. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(a)}& 4& 1& 3& 2\end{array}$
2. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(b)}& 3& 1& 4& 2\end{array}$
3. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(c)}& 1& 4& 3& 2\end{array}$
4. $\begin{array}{ccccc}\text{Sets}& \text{(A)}& \text{(B)}& \text{(C)}& \text{(D)}\\ \text{(d)}& 3& 4& 1& 2\end{array}$