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Physics Mock 1 for IIT JEE

Utkarsh Gupta — Mon, 12 Nov 2018 08:30:38 +0000

Physics Mock Test for IIT JEE by KFDN

Physics Mock Test is brought to you by Kailasha Foundation- Fun & Learn Portal to help you boost yourself for JEE, and other engineering entrance exams with our specially tailored content from the subject. With this test, we have delivered questions from the syllabus of chemistry for IIT JEE to you in an interactive mock test environment which will help you for the preparation of your Exam.

Instructions:

You have 1 hour to attempt this test.
All questions carry equal marks and each correct answer will give you 4 marks.
You will be awarded minus one mark for each wrong answer.

START YOUR TEST

Other mocks for your preparation

IIT JEE Mock 2

IIT JEE Mock 1

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Chemistry Mock 1 for IIT JEE

Utkarsh Gupta — Mon, 12 Nov 2018 07:30:04 +0000

Chemistry Mock Test for IIT JEE by KFDN

Chemistry Mock Test is brought to you by Kailasha Foundation- Fun & Learn Portal to help you boost yourself for JEE, and other engineering entrance exams with our specially tailored content from the subject. With this test, we have delivered questions from the syllabus of chemistry for IIT JEE to you in an interactive mock test environment which will help you for the preparation of your Exam.

Instructions:

You have 1 hour to attempt this test.
All questions carry equal marks and each correct answer will give you 4 marks.
You will be awarded minus one mark for each wrong answer.

START YOUR TEST

Other mocks for your preparation

IIT JEE Mock 2

IIT JEE Mock 1

Kailasha Foundation – Bringing Solutions To You

The post Chemistry Mock 1 for IIT JEE appeared first on Kailasha Foundation.

Heisenberg’s Uncertainty Principle and Quantum Mechanical Model

Utkarsh Gupta — Fri, 26 Oct 2018 05:30:41 +0000

Heisenberg’s Uncertainty Principle

According to this principle, it is impossible to determine the position and momentum of a small microscopic moving particle like an electron with absolute accuracy or certainty.

According to him, the uncertainty in position (Δx) and uncertainty in momentum (Δp = m.Δv) is equal to or greater than h/4π.

Mathematically,

Δx. Δp ≥ h/4π

Explanation of Heisenberg’s uncertainty principle

Suppose we attempt to measure both the position and momentum of an electron, to pinpoint the position of the electron we have to use light so that the photon of light strikes the electron and the reflected photon is seen in the microscope.

As a result of the hitting, the position, as well as the velocity of the electron, are disturbed. The accuracy with which the position of the particle can be measured depends upon the wavelength of the light used. The uncertainty in position is ± λ.

The shorter the wavelength, the greater is the accuracy. But shorter wavelength means higher frequency and hence higher energy. This high energy photon on striking the electron changes its speed as well as direction. But this is not true for the macroscopic moving particle.

Hence Heisenberg’s uncertainty principle is not applicable to macroscopic particles.

Quantum Mechanical Model of an atom

In 1926, Ervin Schrodinger developed an atomic model based on the wave and particle nature of electron which is known as the quantum mechanical model of the atom.

Schrodinger derived an equation which describes wave motion of an electron. The differential equation given by Schrodinger is

where x, y, z are certain coordinates of the electron, m = mass of the electron E = total energy of the electron. V = potential energy of the electron; h = Planck’s constant and Ψ (psi) = wave function of the electron.

The significance of Wave Function Ψ:

The wave function may be regarded as the amplitude function expressed in terms of coordinates x, y, and z. The wave function may have positive or negative values depending upon the value of coordinates.

The main aim of Schrodinger equation is to give solution for probability approach. When the equation is solved, it is observed that for some regions of space the value of Ψ is negative.

But the probability must be always positive and cannot be negative, it is thus, proper to use Ψ2 in favour of Ψ.

The significance of Ψ²:

It is probability factor. It describes the probability of finding an electron in a space. Space, where the probability of finding an electron is maximum, is described as an orbital.

The important point of the solution of the wave equation is that it provides a set of numbers called quantum numbers which describe energies of the electron in atoms, information about the shapes and orientations of the most probable distribution of electrons around the nucleus.

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Quantum Numbers

Utkarsh Gupta — Fri, 26 Oct 2018 05:30:17 +0000

Since a sub-shell can only contain two electrons so, an atom generally has a large number of shells and sub-shells.

The different sub=shells are differentiated from each other on the basis of their size, shape, orientation and these parameters are expressed in terms of different quantum numbers.

Quantum numbers are basically set of numbers associated with an electron with the help of which one can get complete information about that electron. There are four quantum numbers. These four quantum numbers define the location, energy, type, and shape of orbital and spin of the electron.

(1) Principal Quantum Number (n):

This quantum number defines that electron is in which shell and also it tells us about the approximate distance of electron from the nucleus.

Also, for a value of n, the maximum number of electron that can be presented in that shell is 2n².

Shell	Principal Quantum Number (n)	Maximum number of electrons
K	1	2
L	2	8
M	3	18
N	4	32

(2) Azimuthal Quantum Number (l):

This quantum number is also called Angular Quantum number and it represents the number of sub-shell present in the shell.

The sub-shells are represented by s, p, d, f…

This quantum number also represents the shape of the sub-shells or orbital.

The orbital angular momentum of an electron can be calculated by using the formula

For a given shell having principal quantum number n, there are ‘n’ possible sub shells having values ranging from 0 to ‘n-1’.

(3) THE MAGNETIC QUANTUM NUMBER (m):

Because of the angular movement of an electron around the nucleus, the electric field is generated. The magnetic field is produced by this electric field.

Under the influence of the external magnetic field, the electrons of a sub shell can orient them in certain preferred regions of space around the nucleus called orbitals.

The magnetic quantum number determines the number of preferred orientations of the electron present in a sub-shell. The magnetic quantum number determines the number of preferred orientations of the electron present in a sub-shell.

The values of magnetic quantum number depends upon the Azimuthal quantum number l.

The magnetic quantum number ‘m’ can have all integer values between -l to +l including zero.

Thus m can be – 1 , 0 , + 1 for l = 1. Total values of m associated with a particular value of l is given by (2l + 1).

(4) THE SPIN QUANTUM NUMBER (S):

An electron not only revolves but also spin about its own axis in an atom. There are two possibilities for spinning of electron i.e. clockwise or anti-clockwise. Therefore for any particular value of the magnetic quantum number, the spin quantum number can have two values.

The two values of spin quantum number +1/2 and -1/2 are represented by two arrows pointing in opposite directions, i.e. ↑ and ↓.

When an electron goes to a vacant orbital, it can have a clockwise or anti clockwise spin

i.e., + 1/2 or – 1/2

This quantum number helps to explain the magnetic properties of the substances.

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Electronic Configuration

Utkarsh Gupta — Thu, 25 Oct 2018 09:30:33 +0000

We know that an orbital can accommodate two electrons only and there are many atoms having more than two electrons and hence multiple orbitals are filled to accommodate all the electrons.

The atom is built up by filling electrons in various orbitals according to the following rules mentioned below:

Aufbau Principle:

According to Aufbau Principle, electrons are added to the orbitals in order of their increasing energy starting with the orbital of lowest energy i.e. 1s.

The increasing order of various orbitals in terms of energy is given below:

1s , 2s , 2p , 3s , 3p , 4s , 3d , 4p , 5s , 4d , 5p , 6s , 4f , 5d , 6p , 5f , 6d , 7p ………..

Starting from the top, the direction of the arrows gives the order of filling of orbitals.

Alternatively, the sum of Principal and Azimuthal quantum number can be used to compare the energy of various orbitals. This is called (n+l) rule,

According to this rule,

“In a neutral isolated atom, orbital with lower energy will have the lower value of (n+l). ”

However, “if the two different types of orbitals have the same value of (n+ l), the orbitals with the lower value of n has lower energy.”

Pauli’s Exclusion Principle:

According to this principle, an orbital can contain maximum two electrons and these two electrons must have opposite spin.

or Alternatively, it can be said that no two electrons in an atom can have the same set of values of all four quantum numbers.

Hund’s Rule of Maximum Multiplicity:

Hund’s rule is used to fill an electron in the equal energy (degenerate) orbitals of the same sub shell (p, d, and f ).

According to this rule,

“Electron pairing in p, d and f orbital cannot occur until each orbital of a given sub shell contains one electron each or singly occupied.”

This is due to the fact that electrons being identical in charge, repel each other when present in the same orbital.

This repulsion can, however, be minimised if two electrons move as far apart as possible by occupying different degenerate orbitals.

All the electrons in a degenerate set of orbitals will have the same spin.

Electronic Configuration of Elements

Electronic configuration of an atom or element is the distribution of electrons of the atom in various orbitals of an atom.

The electronic configuration can be represented with the notation as shown below.

Half Filled and Completely Filled Orbitals

Fully filled and half filled orbitals are relatively more stable.

For e.g. Chromium having atomic number Z = 24 and its expected electronic configuration should be

1s²2s²2p⁶3s²3p⁶4s²3d⁴

However actual electronic configuration of Chromium is

1s²2s²2p⁶3s²3p⁶4s¹3d⁵

But a shift of one electron from lower energy orbital of 4s to higher energy orbital 3d makes 3d orbital half filled and imparts more stability to chromium atom.

Similarly the electronic configuration of Cu (Z=29) is

1s²2s²2p⁶3s²3p⁶4s¹3d¹⁰

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Bohr’s Atomic Model

Utkarsh Gupta — Tue, 23 Oct 2018 05:30:46 +0000

Bohr developed a model of an atom by modifying Rutherford’s model of an atom. The important postulates given were:

An atom consists of a dense nucleus situated at the centre with the electron revolving around it in circular orbits without emitting any energy.
The force of attraction between the nucleus and an electron is equal to the centrifugal force of the moving electron.
The permitted angular momentum (mvr) in electron orbit is integral multiple h/2π.

i.e. mvr = nh/2π.

Where, m = mass of electron, v = velocity of electron, n = orbitnumber in which electron is present, r = radius of the orbit, h = Planck’s constant.

An electron neither lose nor gain energy while revolving in an orbit. Since, there is no energy loss or gain, so these are called stationary orbits.
Each stationary orbit has a fixed definite amount of energy and these stationary orbits are also called energy levels. The greater is the distance of orbit from the nucleus, more is the energy associated with it. These energy levels are numbered as 1, 2, 3 4 (1 is nearest to the nucleus) or K, L, M, N etc.
In the stable state of an atom, electron continues to move in a particular orbit without losing any energy.
If energy is supplied to electrons in any form, the electron jumps from the lower energy level to higher energy level by absorbing one or more quanta of energy. When electrons are in higher energy state then the atom is said to be in an excited state. The energy of quanta absorbed is equal to the difference in the energy of the two levels in which transition occurs.
Excited states are less stable and hence electron always jumps back to the ground state by releasing the energy.

Energy absorbed or released in an electron jump, (∆E) is given by

∆E = E₂ – E₁ =hν

Where E₁and E₂are the energies of the electron in the first and second orbit or energy level and ν will be the frequency of radiation absorbed or released.

Radius of Atom using Bohr Model:

Let us consider an electron having mass ‘m’ and charge ‘e’ is revolving around a nucleus having atomic number Z with tangential velocity v. So charge in the nucleus will be Ze (e is the charge of the proton).

As per Coulomb’s Law, the electrostatic force of attraction between electron and nucleus will be given by

Energy of electron in nth orbit

The energy of an electron at any time in an atom will be the sum of its kinetic energy as well its potential energy.

Now, the Kinetic energy of the electron will be given by (1/2)mv²

Hydrogen spectrum by Bohr’s theory

As per Bohr’s atomic theory electron neither emits nor absorbs energy, as long as it stays in a particular orbit. However, when an atom absorbs energy, the electron in the atom may jump from the ground state to some higher energy level i.e., exited state.

But as the life time of the electron in the excited state is short, it returns to the ground state in one or more jumps.

During each jump, energy is emitted in the form of a photon of light of definite wavelength or frequency. The frequency of the photon of light thus emitted depends upon the energy difference of the two energy levels concerned (n₁, n₂), and the frequency is given by

Achievement of Bohr’s Theory

(i) The experimental value of radius and energy of hydrogen atom were good in agreement with that calculated with Bohr’s theory.

(ii) Bohr’s model was able to explain the emission and absorption spectra of hydrogen and hydrogen like an atom.

Limitations of Bohr Model of Atom

(i) Bohr’s model was unable to explain the spectrum of atoms having more than one electron in their orbit.

(ii) Bohr’s model was unable to explain the Zeeman (Splitting of the spectral line into several component by the application of magnetic field) and Stark effect (Splitting of the spectral line into several component by the application of electric field).

(iii) Dual character of electron suggested by De Broglie was not considered in Bohr’s model of an atom.

(iv) TheHeisenberg’s Uncertainty Principle contradicts the Bohr’s postulate that “electrons revolve in well-defined orbits around the nucleus with well-defined velocities”.

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Thermodynamics Mock – 3

Utkarsh Gupta — Thu, 20 Sep 2018 15:29:02 +0000

Thermodynamics Mock Test by KFDN

“Thermodynamics” Mock Test is brought to you by Kailasha Foundation- Fun & Learn Portal to help you boost yourself for JEE, NEET, and other competitive exams with our specially tailored content from the subject. With this test, we have delivered 20 questions from the topic of Thermodynamics to you in an interactive mock test environment which will help you for the preparation of your Exam.

Instructions:

You have 20 minutes to attempt this test.
All questions carry equal marks and each correct answer will give you 4 marks.
You will be awarded minus one mark for each wrong answer.

START YOUR TEST

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The post Thermodynamics Mock – 3 appeared first on Kailasha Foundation.

Kinematics Mock – 1

Utkarsh Gupta — Fri, 14 Sep 2018 11:30:33 +0000

Kinematics Mock Test by KFDN

“Kinematics” Mock Test is brought to you by Kailasha Foundation- Fun & Learn Portal to help you boost yourself for JEE, NEET, and other competitive exams with our specially tailored content from the subject. With this test, we have delivered 20 questions from the topic of Kinematics to you in an interactive mock test environment which will help you for the preparation of your Exam.

Instructions:

You have 20 minutes to attempt this test.
All questions carry equal marks and each correct answer will give you 4 marks.
You will be awarded minus one mark for each wrong answer.

START YOUR TEST

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The post Kinematics Mock – 1 appeared first on Kailasha Foundation.

Thermodynamics Mock – 2

Utkarsh Gupta — Wed, 12 Sep 2018 05:30:22 +0000

Thermodynamics Mock Test by KFDN

Instructions:

You have 20 minutes to attempt this test.
All questions carry equal marks and each correct answer will give you 4 marks.
You will be awarded minus one mark for each wrong answer.

START YOUR TEST

Kailasha Foundation – Bringing Solutions To You