Visualising Orbitals

Q. Which of the following statements regarding an orbital is correct?

1. An orbital is a definite trajectory around the nucleus in which electrons can move
2. An orbital always has a spherical trajectory
3. An orbital is a region around the nucleus where the probability of finding all the electrons is 90% to 95%
4. An orbital is characterized by three distinct quantum numbers n, l and m

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. 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 number of nodes in graph $1,2,3$ and 4 respectively are:

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

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

Q. An electron in an atom:

1. has a fixed position
2. revolves inside the nucleus
3. emits energy continuously
4. revolves in circular orbit

Q.
The number of nodes in graph $1,2,3$ and 4 respectively are:

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

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)