Shapes of Orbitals and Nodes

Q.

How to identify whether a compound will undergo d-d transitions or not? Please explain with examples!

Q. The ratio of radii of first Bohr orbits of $H{e}^{+},L{i}^{2+}$ and $B{e}^{3+}$ is:

1. $6:4:3$
2. $6:3:2$
3. $2:6:3$
4. $3:2:6$

Q. The ratio of the wavelengths of last lines of Balmer and Lyman series is:

1. $4:1$
2. $27:5$
3. $3:1$
4. $9:4$

Q. Which of the following orbital has 2 radial as well as 2 angular nodes.

1. 3s

2. 5d
3. 3d
4. 4d

Q. The wave function $\left(\Psi \right)$ of $2s$ is given by:
${\Psi }_{2s}=\frac{1}{2\sqrt{2\pi }}{\left(\frac{1}{a_0}\right)}^{\frac{1}{2}}\{2-\frac{r}{a_0}\}{e}^{\left(-r/a_0\right)}$
Where $a_0$ is Bohr's radius. If the radial node in $2s$ is at $r_0,$ then find $r_0$ in terms of $a_0$.

1. $a_0$
2. $2a_0$
3. $3-(5{)}^{\frac{1}{2}}{a}_0$
4. None of these

Q. For a 3d-orbital, the orbital angular momentum is

1. $\frac{2h}{2\pi }$
2. $Zero$
3. $\sqrt{2}\frac{h}{2\pi }$
4. $\sqrt{6}\frac{h}{2\pi }$

Q. The number of nodal planes in the $p_x$ orbital is/are:

1. One
2. Two
3. Three
4. Zero

Q.

The $H$-like species $L{i}^{2+}$ is in spherically symmetrical state $S_1$ and one radial node. Upon absorbing light, the ion undergoes transition to state $S_2$. The state $S_2$ has one radial node and it has the same energy as the ground state energy of a $hydrogen$ atom.

The orbital angular momentum quantum number of state $S_2$ is:

1. $0$
2. $1$
3. $2$
4. $3$

Q.

Total number of nodes = _____

1. l

2. n - 1

3. n - l - 1

4. l - 1

Q. Which of the following radial probability curve is correct for a 3p - orbital? (Assume that all graphs have been plotted for the same parameters. In all these curves principal quantum nuber < 4)

1. None of these
2. 
3. 
4. 

Q.

What is a node?

Q. The number of radial nodes in $3s$ and $2p$ orbitals respectively are:

1. 2, 0
2. 0, 2
3. 1, 2
4. 2, 1

Q. Which of the following orbitals has a zero probability of finding electrons in the $XY$ plane?

1. $p_z$
2. $d_{x^2-y^2}$
3. $p_x$
4. $d_{z^2}$

Q. The radial wave function for an orbital in a hydrogen atom is:
$\psi =\frac{1}{16\sqrt{3}}{\left(\frac{1}{a_0}\right)}^{\frac{3}{2}}\left[\right(x-1\left)\right(x^2-8x+12\left)\right]e^{-\frac{x}{2}}$
where, $x=\frac{2r}{a_0};a_0=$ radius of first Bohr's orbit. The minimum and maximum position of radial nodes from the nucleus are:

1. $\frac{a_0}{2},a_0$
2. $\frac{a_0}{2},4a_0$
3. $a_0,3a_0$
4. $\frac{a_0}{2},3a_0$

Q. What is the maximum wavelength of line of Balmer series of hydrogen spectrum? $(R=1.09\times {10}^7{m}^{-1})$

1. 400 nm
2. 660 nm
3. 486 nm
4. 434 nm

Q.

The number of radial nodes and angular nodes is the same in which of the following orbital/orbitals?
(A) 3p (B) 4p (C) 5d (D) 6f

1. A only
2. D only
3. B and C both
4. A and C both

Q. The radial part of an atomic orbital wave function depends on:

1. n
2. n and l
3. n, l, and m
4. l and m

Q.

Which of the following pairs of d-orbitals will have electron density along the axis?

1. $d_{xz},d_{yz}$

2. $d_{z^2},d_{x^2-y^2}$

3. $d_{z^2},d_{xz}$

4. $d_{xy},d_{x^2-y^2}$

Q. Match the following :

$\left(1\right)$	Dumbbell shape	$\left(p\right)$	s-orbital
$\left(2\right)$	Double dumbbell shape	$\left(q\right)$	p-orbital
$\left(3\right)$	Complex shape	$\left(r\right)$	d-orbital
$\left(4\right)$	Sherical	$\left(s\right)$	f-orbital

1. 1-q, 2-s, 3-r, 4-p
2. 1-q, 2-r, 3-s, 4-p
3. 1-r, 2-q, 3-s, 4-p
4. 1-q, 2-r, 3-p, 4-s

Q.

Does the VSEPR theory predict that ${\mathrm{XeF}}_2$ is linear?

Q.

Question 26

Calculate the total number of angular nodes and radical nodes and radical nodes present in 3p orbital.

Q. The orbital angular momentum of $3p$ electron is :

1. $\sqrt{3}h$
2. $\sqrt{6}h$
3. $Zero$
4. $\sqrt{2}\frac{h}{2\pi }$

Q.

What is the difference between nodal surfaces and nodal planes?

Q. If number of close packed spheres is N, then number of Tetrahedral voids is 2N and number of Octahedral voids is N. Why is it so?

Q. Which of the following statements is true regarding the $d{z}^2$ orbital?

1. It is a double-dumble shaped along the x and the z-axis
2. It is a double dumbbell shaped in between the y and z- axis
3. It is single dumbbell along the z - axis, with a donut like ring along the nucleus along the x-y plane.
4. It is a double dumbbell shaped in between the x and y - axis

Q. What will be the radius of third Bohr's orbit of $B{e}^{3+}$ ion, if the radius of second Bohr's orbit of hydrogen atom is $r_2$?

1. $9r_2$
2. $\frac{9r_2}{8}$
3. $\frac{9r_2}{16}$
4. $\frac{9r_2}{4}$

Q.

How Many Radial Nodes Are Present In $3p$ Orbital?

Q. The quantum number which determines the shape of an orbital is:

1. magnetic quantum number
2. Azimuthal quantum number
3. principal quantum number
4. spin quantum number

Q. Number of nodal planes (planes of zero electron density) in the $d_{xy}$ orbital is:

1. 1
2. 2
3. 0
4. 4

Q. Which of the following orbital is non-directional?

1. $s$
   
2. $p$
   
3. $d$
   
4. $f$