Visualising Orbitals

Q.

What do you mean by the dual nature of an electron?

Q. An accelerated electron has a speed of $5\times {10}^{6}m{s}^{-1}$ with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is $x\times {10}^{-9}m$. The value of x is .
[Use mass of electron $=9.1\times {10}^{-31}kg,h=6.63\times {10}^{-34}Js,\pi 3.14$]

Q. Prove that path of projectile is parabolic?

Q. For azimuthal quantum number $l=3$, the maximum number of electrons will be:

1. $2$
2. $6$
3. $0$
4. $14$

Q. A ball weighing $10g$ is moving with a velocity of $90m{s}^{-1}.$ If the uncertainty in its velocity is $5\%$, then the uncertainty in its position is $\times {10}^{-33}m.$ (Rounded off to the nearest integer)

[Given : $h=6.63\times {10}^{-34}Js$]

Q. P is the probability of finding a 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is $4\pi r^{2}dr$. The qualitative sketch of the dependence of P on r is

1. 
2. 
3. 
4. 

Q.

The energy required to ionize a hydrogen-like ion in its ground state is $9$ Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state?

1. 8.6

2. 11.4

3. 24.2

4. 35.8

Q.

What is the correct model is atom?

Q. Which quantum number defines the orientation of orbital in the space around the nucleus?

1. Azimuthal quantum number $\left(l\right)$
2. Principal quantum number $\left(n\right)$
3. Magnetic quantum number $\left(m_l\right)$
4. Spin quantum number $\left(m_s\right)$

Q. In which of the following orbitals, nodal plane is absent?

1. $4s$
2. $4d_{z^2}$
3. $4d_{x^2-y^2}$
4. $4d_{zx}$

Q. What is the transition temperature of $\alpha$ and $\beta$-sulphur?

1. ${369}^{\circ }C$
2. ${369}^{\circ }F$
3. ${95.5}^{\circ }C$
4. ${95.5}^{\circ }F$

Q. Which of the following pair of orbitals possess two nodal planes

1. p_xy, d_x²-y²
2. d_xy, d_zx
3. p_xy, d_zx
4. p_yz, d_x²-y²

Q. Which of the following orbitals has two spherical nodes?

1. $2s$
2. $4s$
3. $3d$
4. $6f$

Q.

Distinguish between orbital and subshell.

Q. The Schrodinger wave function for Hydrogen atom of 4s orbital is given by:
${\Psi }_{4s}=\frac{1}{16\sqrt{3}}{\left(\frac{1}{a_0}\right)}^{\frac{3}{2}}\left[\right(\sigma -1\left)\right({\sigma }^2-8\sigma +12\left)\right]e^{-\sigma /2}$
where $a_0$ = $1^{st}$ Bohr radius and $\sigma =\frac{2r}{a_o}$.

The distance from the nucleus where there is no radial node will be:

1. $r=3a_0$
2. $r=a_0$
3. $r=2a_0$
4. r = $\frac{a_0}{2}$

Q. The radial probability distribution curve of an orbital of H has 4 local maxima. If the orbital has 3 angular nodes, then the orbital will be

1. 7d
2. 8d
3. 8f
4. 7f

Q. The number of radial nodes and angular nodes for d-orbital can be represented as:

1. $(n-2)\text{radial nodes}+1\text{angular node}=(n-1)\text{total nodes}$
2. $(n-3)\text{radial nodes}+2\text{angular nodes}=(n-l-1)\text{total nodes}$
3. $(n-1)\text{radial nodes}+1\text{angular node}=(n-1)\text{total nodes}$
4. $(n-3)\text{radial nodes}+2\text{angular nodes}=(n-1)\text{total nodes}$

Q. Consider the reaction $A\rightleftharpoons B$ at $1000K$ . At time $t$ , the temperature of the system was increased to $2000K$ and the system was allowed to reach equilibrium. Throughout this experiment, the partial pressure of $A$ was maintained at $1bar$ . Given below is the plot of the partial pressure of $B$ with time.
What is the ratio of the standard Gibbs energy of the reaction at $1000K$ to that at $2000K$ ?

Q.

$2P\left(g\right)\to 4Q\left(g\right)+R\left(g\right)+S\left(l\right)$
The decomposition of compound P, at temperature T follows first order kinetics.
After 30 minutes, the total pressure developed in the closed vessel is found to be $310mmHg$ and the total pressure observed at the end of reaction is $610mmHg$.
Calculate the total pressure of the vessel after 75 minutes, if volume of liquid (S) is supposed to be negligible.
Given: Vapour pressure of $S\left(l\right)$ at temperature, $T=30mmHg$
Take:
$e^{0.4}=1.5$

1. $P_t=37.9mmHg$

2. $P_t=377.5mmHg$

3. $P_t=179.55mmHg$

4. None of these

Q. Given : The mass of electron is $9.11\times {10}^{–31}kg$, Planck constant is $6.626\times {10}^{–34}Js$, the uncertainty involved in the measurement of velocity within a distance of $0.1\AA$ is:

1. $5.79\times {10}^{5}m{s}^{-1}$
2. $5.79\times {10}^{6}m{s}^{-1}$
3. $5.79\times {10}^{7}m{s}^{-1}$
4. $5.79\times {10}^{8}m{s}^{-1}$

Q. How many spherical nodes are there in $4s$ – sub-shell?

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

Q.

The region having the maximum probability of finding an electron in space is known as ___.

Q. The uncertainty in the velocity of a cricket ball of mass $100\text{g}$, when uncertainty in its position is of the order of $1\stackrel{o}{\text{A}}$, would be :
(Given : $h=6.626\times {10}^{-34}\text{J-s},\pi =3.14,\frac{6.626}{3.14}=2.11$ )

1. $\ge 5.27\times {10}^{-24}{\text{ms}}^{-1}$
2. $\ge 2.35\times {10}^{-23}{\text{ms}}^{-1}$
3. $\ge 3.16\times {10}^{-22}{\text{ms}}^{-1}$
4. $\ge 8.51\times {10}^{-24}{\text{ms}}^{-1}$

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. The equilibrium constant $K_p$( in atm) for the reaction is $2.46$ at $7$ atm and $300\text{K}$.
$A_2\left(g\right)\rightleftharpoons B_2\left(g\right)+C_2\left(g\right)$
Calculate the average molar mass (in g/mol) of an equilibrium mixture.
Given: Molar mass of $A_2,B_2$and $C_2$ are $70,49$ and $21\text{g/mol}$ respectively.
(Given $R=0.082{\text{L atm K}}^{-1}{\text{mol}}^{-1},\sqrt{0.1}\approx 0.3$

1. $56.7$
2. $45$
3. $40$
4. $37.5$

Q.

Which of the following pairs of d-orbitals have electron density along the axis? ${\mathrm{dz}}^2,\mathrm{dxz}\mathrm{dxz},\mathrm{dyz}{\mathrm{dz}}^2,{\mathrm{dx}}^2–{\mathrm{y}}^2\mathrm{dzy},{\mathrm{dx}}^2–{\mathrm{y}}^2$

Q. Which of the following system is correct?

1. For any cyclic process, $\Delta U=0$
2. $(\frac{\delta U}{\delta V}{)}_T=\frac{a}{V^2}$ for 1 mole of a gas obeying van der waal's equation
3. $\overline{C_p}=\infty$ for water when it is in equilibrium with vapour at $1atm$ pressure and $373K$
4. For any real gas, the molar internal energy can be given as $\frac{3}{2}R$

Q. Select the correct statement(s):

1. Radial function [R(r)] a part of wave function is dependent on quantum number n only
   
2. Angular function depends only on the direction and is independent to the distance from the nucleus
3. ${\psi }^2(r,\theta ,\varphi )$ is hte probability density of finding the electron at a particular point in space
4. Radial distribution function $\left(4\pi r^2{R}^2\right)$ gives the probability of the electron being present at a distance r from the nucleus

Q. For the equilibrium $Ni{O}_{\text{(s)}}+C{O}_{\text{(g)}}\rightleftharpoons N{i}_{\text{(s)}}+C{O}_{2\text{(g)}},\Delta G^0\left({\text{J mol}}^{-1}\right)=-20,700-11.97\text{T}$. Calculate the temperature (in K) at which the product gases at equilibrium at $1\text{atm}$ will contain $400\text{ppm}$ (parts per million) of carbon monoxide:( upto two decimal where $R=8.314{\text{J K}}^{-1}{\text{mol}}^{-1}$)

Q. The magnetic quantum number of an atom is related to the

1. Size of the orbital
2. Spin angular momentum
3. Orbital angular momentum
4. Orientation of the orbital in space