Schrodinger Equation

Q.

Study the extract of the periodic table given below and answer the questions that follow. Give the alphabet corresponding to the elements in the question. DO NOT repeat an element .

A

C

D

E

B

G

F

1. Which element forms electrovalent compound with G?
2. The ion of which element will migrate towards the cathode during electrolysis?
3. Which non metallic element has the valency of 2?
4. Which is an inert gas?

Q. The correct order for the wavelength of absorption in the visible region is-

1. $\left[Ni\right(N{O}_2{)}_6{]}^{4-}<\left[Ni\right(N{H}_3{)}_6{]}^{2+}<\left[Ni\right(H_{2}O{)}_6{]}^{2+}$
2. $\left[Ni\right(N{O}_2{)}_6{]}^{4-}<\left[Ni\right(H_{2}O{)}_6{]}^{2+}<\left[Ni\right(N{H}_3{)}_6{]}^{2+}$
3. $\left[Ni\right(H_{2}O{)}_6{]}^{4-}<\left[Ni\right(N{H}_3{)}_6{]}^{2+}<\left[Ni\right(N{O}_2{)}_6{]}^{4-}$
4. $\left[Ni\right(N{H}_3{)}_6{]}^{2+}<\left[Ni\right(H_{2}O{)}_6{]}^{2+}<\left[Ni\right(N{O}_2{)}_6{]}^{4-}$

Q. Boron is unable to form $B{F}_6^{3-}$ ion. Explain.

Q.

What is the symbol of aluminium ion?

Q. The complete wave function of an orbital of hydrogen is given as $\psi =\frac{1}{4a_0\sqrt{2\pi a_0}}(2-\frac{r}{a_0})e^{\frac{-r}{2a_0}}$,
($a_0$ is first Bohr radius)
Which of the following option(s) is/are correct?

1. Orbital may be 3p
2. Angular node is at $2a_0$ from nucleus
3. Ratio of density of probability of finding electron at distance $a_0$ to nucleus is $\frac{e^{-1}}{4}$
4. Orbital has a total of one node

Q. The wave function of hydrogen atom with its electron in the 2p state varies with direction as well as distance from the nucleus. What is the probability of a 2p electron, for which ml=0, existing in xy plane is 0.Why?

Q. Consider following Schrodinger wave equation for an orbital of hydrogen atom.
$(a_0$ is first Bohr radius)
$\Psi =\frac{\sqrt{2r}}{81a_0^2\sqrt{\pi a_0}}(6-\frac{r}{a_0})e^{\frac{-r}{3a_0}}cos\theta$

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \left(I\right)& \text{Which orbital is this?}& \left(P\right)& 1\\ \left(II\right)& \text{Number of total node(s)}& \left(Q\right)& 2\\ \left(III\right)& \text{Nodal plane}& \left(R\right)& 3p_z\\ \left(IV\right)& \text{Number of radial node(s)}& \left(S\right)& 3p_x\\ & & \left(T\right)& \text{XY plane}\\ & & \left(U\right)& \text{YZ plane}\end{array}$

Match the correct combination considering List-I and List-II

1. (III), (T) and (IV), (P)
   
   
2. (III), (U) and (IV), (P)
3. (III), (T) and (IV), (Q)
4. (III), (U) and (IV), (Q)

Q. What is the Schrodinger's equation?

Q. Which of the following statements is incorrect?

1. Wave functions are found by solving Schrodinger wave equation
2. Two spectral lines of an element must have the same wave number
3. Energy of an electron at infinite distance is zero yet it is maximum
4. The position and momentum of a large rolling ball can be measured accurately.

Q. Identify the correct order of wavelength of light absorbed for the following complex ions:
$\begin{array}{cccc}\left[Co\right(H_{2}O{)}_6{]}^{3+};& \left[Co\right(CN{)}_6{]}^{3-};& \left[Co\right(I{)}_6{]}^{3-};& \left[Co\right(en{)}_3{]}^{3+}\\ I& II& III& IV\end{array}$

1. III > I > IV >II
2. II > IV > I >III
3. III > I > II >IV
4. I > III > IV >II

Q.

In a H - atom, the transition takes place form L to K shell. If R = $1.08\times {10}^7{m}^{-1}$. The wave length of the light obsorbed in nearly:

1. 1850 A⁰

2. 1650 A⁰

3. 4400 A⁰

4. 1250 A⁰

Q. Consider following Schrodinger wave equation for an orbital of hydrogen atom.
$(a_0$ is first Bohr radius)
$\Psi =\frac{\sqrt{2r}}{81a_0^2\sqrt{\pi a_0}}(6-\frac{r}{a_0})e^{\frac{-r}{3a_0}}cos\theta$

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \left(I\right)& \text{Which orbital is this?}& \left(P\right)& 1\\ \left(II\right)& \text{Number of total node(s)}& \left(Q\right)& 2\\ \left(III\right)& \text{Nodal plane}& \left(R\right)& 3p_z\\ \left(IV\right)& \text{Number of radial node(s)}& \left(S\right)& 3p_x\\ & & \left(T\right)& \text{XY plane}\\ & & \left(U\right)& \text{YZ plane}\end{array}$

Match the correct combination considering List-I and List-II

1. (I), (R) and (II), (P)
   
2. (I), (S) and (II), (Q)
3. (I), (S) and (II), (P)
4. (I), (R) and (II), (Q)

Q. Consider the following orbitals, $3s,2p_x,4d_{xy},4d_{z^2},3d_{x^2-y^2},3p_y,4s,4p_z$ and find total number of orbital(s) having even number of nodal plane.

Q. A permissible solution to the Schrödinger wave equation gave an idea of quantum numbers.

1. 4
2. 3
3. 2

Q. Identify the correct order of wavelength of light absorbed for the following complec ions
$\left[Co\right(H_{2}O{)}_6{]}^{3+};Co(CN{)}_6{]}^{3-};[Co{I}_6{]}^{3-};\left[Co\right(en{)}_3{]}^{3+}IIIIIIIV$

1. $III>I>IV>II$
2. $II>IV>I>II$
3. $III>I>II>IV$
4. $I>III>IV>II$

Q. What is Schrödinger equation?

Q.

A permissible solution to the schrodigner wave equation gave an idea of _____ quantum numbers.

1. 4

2. 1

3. 2

4. 3

Q.

The wave function $\psi$ in the Schrodinger wave equation represents

1. Probability of the electron

2. Amplitude of the wave

3. Frequency of the wave

4. Speed of the wave

Q.

What is the formula for a sine wave?

Q. As compared to the $1s$ electron of $H-$ atom in ground state, which of the following properties appear(s) in the radial probability density of electron of $H-$ atom in first excited state ?

1. Spherical node appears
2. Electron probability density is highest in the vicinity of the nucleus
3. Probability density drops to zero after maximum probability is reached
4. Probability density rises to second highest value

Q. The wave function for $1s$ orbital of the hydrogen atom is given by

1. $e$
2. $e^2$
3. $1/e^2$
4. Zero

Q.

Quantum numbers are

1. Solution to schrodinger equation

2. Variable in the atomic model

3. Coordinates of Electron position in an atom

4. State variables of electrons

Q.

The possibility of finding an electron in an orbital was conceived by

1. Rutherford

2. Bohr

3. Heisenberg

4. Schrodinger

Q.

Name the following :

Formula of the compound formed between Aluminum and Oxygen

Q. If an electron of hydrogen atom jumps from $n=4$ to $n=2$. Calculate the energy emitted?

Q. The graph between $|\Psi {|}^2$ and r(radial distance) is shown below. This represents:

1. 2s orbital
2. 3s orbital
3. 1s orbital
4. 2p orbital

Q.

What was Schrodingers discovery?

Q. The wave function for $1s$ orbital of hydrogen atom is given by:
${\psi }_{1s}=\frac{\pi }{\sqrt{2}}{e}^{-r/a_0}$
where, $a_0=$ Radius of first Bohr orbit
$r=$ Distance from the nucleus (Probability of finding the electron varies with respect to it)
What will be the ratio of probabilities of finding the electrons at the nucleus to first Bohr's orbit $a_0$?

1. $e^2$
2. $e$
3. $\frac{1}{e^2}$
4. Zero

Q. What is the ratio of maximum and the middle positions of the radial nodes for an hydrogen atom that has this radial wave equation:
$\psi =k{\left(\frac{1}{a_o}\right)}^{3/2}\left[\right(x-1\left)\right(x^2-8x+12\left)\right]e^{-x/2}$
$x=\frac{2r}{a_o},a_o$ is radius of the first Bohr orbit.

Q. In the Schrodinger wave equation, $\psi$ represents:

1. orbitals
2. wave function
3. amplitude function
4. both B & C