Quantum Number, Configuration And Shape of Orbitals MCQ Quiz in मल्याळम - Objective Question with Answer for Quantum Number, Configuration And Shape of Orbitals - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

• Neils Bohr proposed Bohr's postulate which explained that a nucleus (positively charged) is surrounded by negatively charged electrons.
• According to Bhor, Electron which is moving in an orbital does not lose or radiate energy and atom came as a modification to Rutherford’s model of an atom.
• Postulates of Bohr’s model of an atom are:
  • In an atom, electrons move in a fixed circular path around a positively charged nucleus. This path is known as orbits or shells
  • These orbits or shells have fixed energy.
  • The energy levels are represented by an integer (n = 1, 2, 3, 4, …) known as a principal quantum number.
  • If an electron moves from lower energy level to higher energy level, then it will do so by gaining energy and if it moves from higher energy level to lower energy level then it will do so by losing energy.

Explanation:

• Quantum number are those numbers that designate and distinguish various atomic orbitals and electrons present in an atom.
• There are four types of quantum number:
• The angular quantum number determines the three-dimensional shape of the orbital quantum number.
  • Denoted by the symbol ‘l’ is also known as orbital angular momentum or subsidiary quantum number.
  • It defines the three-dimensional shape of the orbital.
• Principal quantum number
  • ​Denoted by the symbol ‘n’.
  • Determines the size and to a large extent the energy of the orbital.
• Magnetic orbital quantum number
  • ​Denoted by the symbol ‘ml’.
  • Gives information about the spatial orientation of the orbital concerning standard set of co-ordinate axis.
• Electron Spin quantum number
  • ​Denoted by the symbol (ms) refers to the orientation of the spin of the electron.

Concept:

• According to Bohr's atomic model, electrons are revolving around the nucleus through a certain fixed circular path called an orbit. These orbits are also called Principal energy levels or shells. These shells are numbered K, L, M, N and so on. These levels are represented by the principal quantum number n. 
• Each shell is further divided into subshells, designated as s, p, d, f  and is assigned an azimuthal quantum number l. 
• An atom consists of a large number of orbitals and these orbitals have different sizes, shapes, orientations, etc. A set of four numbers are required to represent the size of the orbital, the shape of the orbital, the orientation of the orbital, the spin of an electron, etc. and are known as quantum numbers. These quantum numbers are named:

1. Principal quantum number n: represents the name, size and energy of the shell K, L, M, N to which the electron belongs. 
2. Azimuthal quantum number l: describes the subshell s, p, d, f to which an electron belongs and the motion of the electron.
3. Magnetic orbital quantum number m: describes the shape of the orbital occupied by the electron.
4. Spin quantum number s: represents the direction of electron spin around its own axis.

• The energy of the shell goes on increasing as the distance of the shell increases from the nucleus. 
• Each electron moves in the attractive field of the nucleus and experiences an average repulsive charge from the other electrons. This negative charge reduces the actual charge of the nucleus and is called the Effective nuclear charge Z_eff.
• The reduction of the true nuclear charge to the effective nuclear charge by the other electrons is called Shielding.
• The presence of an electron inside the shells of other electrons to get close to the nucleus is called Penetration.

Explanation:

• The closer to the nucleus that an electron can approach or the more it penetrates, the stronger its attraction to the nucleus as the electron-electron repulsion is lesser in the atom.
• Core electrons penetrate more and feel more of the nucleus than the other electrons.
• The values of n orbital and subshell l define how close an electron can approach the nucleus. For example, 2s electron is closer to the nucleus than a 2p electron, therefore it is penetrating the nucleus of the atom more than the 2p electron.
• Therefore, within the same shell value n, the penetration power of an electron in many-electron atoms in subshells l is typically s > p > d > f, s orbitals being the most penetrating and f orbitals are the least penetrating. 
• Since,  2s-electron penetrates closer to the nucleus, it has lower energy as it is bound more tightly than a 2p-electron and therefore, the 2s orbital will be occupied before the 2p orbitals. The pattern of energies with 2s lower than 2p, and in general ns lower than np is a general feature of many-electron atoms. 

Conclusion:

In a given principal quantum n, the penetrating effect decreases in the order s > p > d > f  due to reduced electron-electron repulsions and the proximity of the shells to the nucleus.

Therefore, Reason R is NOT  correct

The correct answer is option 1 i.e 2 and 1 

Number of angular for 4d orbital = 2 

Radial nodes for 4d orbital = 1 

Explanation:

Angular node:

• It is also known as a nodal plane.
• It is a plane that is passing through the nucleus. 

Angular Node = l 

As, Radial Node = n - l - 1 

where, n = 4 

Azimuthal Quantum Number is a Quantum Number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. 

For d orbital the value of Azimuthal Quantum Number = 2 

So, Angular Node = 2  Radial Node = 4 - 2 - 1 = 1

Additional Information

• There are no nodes in the s-subshell of any orbit and also in the first orbit of an atom.
• As the distance of the orbitals from the nucleus increases, the number of nodes also increases.
• Radial nodes are specifically those that are present inside the orbital lobes while angular ones are those that present on the axial planes.

Concept

Nodes are basically some specific region of orbital around the nucleus where the probability of finding an electron is zero.

There are two types of the node; radial node and angular node

Radial node 

• The spherical surface of an orbital where the finding probability of an electron is zero is called the radial node.
• It depends on the principle and azimuthal quantum number of the orbital
• No. Of radial node = n-l-1

Angular node 

• The planar surface  of an orbital where the probability of finding the electron is zero
• It depends only on the azimuthal quantum no.
• No. of angular node = l

Explanation :

For 4d orbital

Principle quantum number (n) = 4

Azimuthal quantum number of d orbital (l) = 2

Thus no. of radial node = n-l-1

=4-2-1

= 1

Further, the number of the angular node for 4d is given as follows,

angular node =l

angular node =2 ( for d subshell l value is 2)

Conclusion :

Therefore, the number of the angular node for 4d orbital is 2

Concept

Nodes are basically some specific region of orbital around the nucleus where the probability of finding an electron is zero.

There are two types of the node; radial node and angular node

Radial node 

• The spherical surface of an orbital where the finding probability of an electron is zero is called the radial node.
• It depends on the principle and azimuthal quantum number of the orbital
• No. Of radial node = n-l-1

Angular node 

• The planar surface  of an orbital where the probability of finding the electron is zero
• It depends only on the azimuthal quantum no.
• No. of angular node = l

Explanation :

For 4d orbital

Principle quantum number (n) = 4

Azimuthal quantum number of d orbital (l) = 2

Thus no. of radial node = n-l-1

=4-2-1

= 1

Further, the number of the angular node for 4d is given as follows,

angular node =l

angular node =2 ( for d subshell l value is 2)

Conclusion :

Therefore, the number of the angular node for 4d orbital is 2

Concept:

The three coordinates that come from Schrdinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers.

These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.

The principal quantum number (n) describes the size of the orbital.

• Orbitals for which n = 2 are larger than those for which n = 1, for example.
• Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom.
• Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n = 1) into an orbital in which it is further from the nucleus (n = 2).
• The principal quantum number therefore indirectly describes the energy of an orbital.

The angular quantum number (l) describes the shape of the orbital.

• Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2).
• They can even take on more complex shapes as the value of the angular quantum number becomes larger.
• There is only one way in which a sphere (l = 0) can be oriented in space.
• Orbitals that have polar (l = 1) or cloverleaf (l = 2) shapes, however, can point in different directions.

We then, therefore,d a third quantum number, known as the magnetic quantum number (m), to describe the orientation in space of a particular orbital.

• (It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.)

Explanation:

Rules Governing the Allowed Combinations of Quantum Numbers

• The three quantum numbers (n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on.
• The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on.
• The angular quantum number (l) can be any integer between 0 and n - 1. If n = 3, for example, l can be either 0, 1, or 2.
• The magnetic quantum number (m) can be any integer between -l and +l. If l = 2, m can be either -2, -1, 0, +1, or +2.

Hence,

n = 3, l = 3, ml = - 2, ms = +\(\frac{1}{2}\)

here n = 3 and l = 3 which is not possible (it can only 0,1,2). There this set is not possible.

Correct answer: 4)

Concept:

There are two kinds of nodes:

(i)angular nodes and

(ii) radial nodes.

• Angular nodes are flat planes at fixed angles). Angular quantum number (l) gives the number of angular nodes in an orbital.
• Radial nodes are spheres (at fixed radius), which is seen with an increase in the principal quantum number.
• The sum of angular and radial nodes gives the total number of nodes of an orbital of an atom 
• The total number of nodes are given by (n–1), i.e., the sum of l angular nodes and (n – l – 1) radial nodes.

Explanation:

No. of radial nodes in an orbital =n-l-1=3-1-1=1" id="MathJax-Element-1-Frame" role="presentation" tabindex="0">=n−l−1

where n= principal quantum number

l= azimuthal quantum number

Number of radial nodes for 3p orbital = 3−1−1

Number of radial nodes for 3p orbital = 3−2

Number of radial nodes for 3p orbital = 1

Conclusion:

Thus, the number of radial nodes present in 3p orbital is 1

Additional Information 

Nodal surface(s) of atomic orbitals

If Y(θ,ϕ) = 0, angular nodes result. Angular nodes are planar or conical.

Number of angular nodes = l

Total number nodal surgace = n -1

If R(r) = 0, radial nodes or spherical nodes result.

Number of radial nodes = n - l - 1

The correct answer is option 1 i.e 2 and 1 

Number of angular for 4d orbital = 2 

Radial nodes for 4d orbital = 1 

Explanation:

Angular node:

• It is also known as a nodal plane.
• It is a plane that is passing through the nucleus. 

Angular Node = l 

As, Radial Node = n - l - 1 

where, n = 4 

Azimuthal Quantum Number is a Quantum Number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. 

For d orbital the value of Azimuthal Quantum Number = 2 

So, Angular Node = 2  Radial Node = 4 - 2 - 1 = 1

Additional Information

• There are no nodes in the s-subshell of any orbit and also in the first orbit of an atom.
• As the distance of the orbitals from the nucleus increases, the number of nodes also increases.
• Radial nodes are specifically those that are present inside the orbital lobes while angular ones are those that present on the axial planes.

Concept:

The three coordinates that come from Schrdinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers.

These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.

The principal quantum number (n) describes the size of the orbital.

• Orbitals for which n = 2 are larger than those for which n = 1, for example.
• Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom.
• Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n = 1) into an orbital in which it is further from the nucleus (n = 2).
• The principal quantum number therefore indirectly describes the energy of an orbital.

The angular quantum number (l) describes the shape of the orbital.

• Orbitals have shapes that are best described as spherical (l = 0), polar (l = 1), or cloverleaf (l = 2).
• They can even take on more complex shapes as the value of the angular quantum number becomes larger.
• There is only one way in which a sphere (l = 0) can be oriented in space.
• Orbitals that have polar (l = 1) or cloverleaf (l = 2) shapes, however, can point in different directions.

We then, therefore,d a third quantum number, known as the magnetic quantum number (m), to describe the orientation in space of a particular orbital.

• (It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.)

Explanation:

Rules Governing the Allowed Combinations of Quantum Numbers

• The three quantum numbers (n, l, and m) that describe an orbital are integers: 0, 1, 2, 3, and so on.
• The principal quantum number (n) cannot be zero. The allowed values of n are therefore 1, 2, 3, 4, and so on.
• The angular quantum number (l) can be any integer between 0 and n - 1. If n = 3, for example, l can be either 0, 1, or 2.
• The magnetic quantum number (m) can be any integer between -l and +l. If l = 2, m can be either -2, -1, 0, +1, or +2.

Hence,

n = 3, l = 3, ml = - 2, ms = +\(\frac{1}{2}\)

here n = 3 and l = 3 which is not possible (it can only 0,1,2). There this set is not possible.

Concept:

As stated by de- Broglie, we know that matter has dual nature, a wave, and a particle.

• The electrons in an atom also possess this dual nature. The wave nature is significant in them due to their small size and negligible mass.
• An orbital describes the wave-like nature of the electron.
• The orbitals are mathematical functions that are used to calculate the probability of finding an electron.
• The probability of finding an electron is maximum in these orbitals.
• The square of the wave functions gives us the probability density of the electrons.
• The wave functions have two parts :
  • Radial - giving us the spread or size of the orbitals
  • Angular- giving us the orientation of the orbitals in space.
• Plotting the wave functions in a three-dimensional coordinate system, we get the shape, size, and orientation of the orbitals.

Explanation:

Wave nature of electrons:

• SchrÖdinger tried to develop the mechanics of electrons based on wave character. This is called wave mechanics.
• Any wave motion is the period variation of some property of the system, which is thus a property of time.
• The displacement of a wave at any point may be expressed as a function of the space coordinates and time 't':

ψ = f(θ,ϕ,t)

• This displacement of the wave about its mean position is known as the amplitude denoted by 'ψ'.
• For simple harmonic motion, such as that exhibited by electrons, the amplitude is given by:

ψ  = sin( kx - ωt ) where, k = wave number, ω  = angular frequency, and x = linear displacement of the particles.

• In wave mechanics, the probability of finding a particle at some point is proportional to the square of its wave function psi at that point ψ².

Hence, the wave function Ψ represents the amplitude function.

Additional Information

• In microscopic systems, if the total energy of the system remains unchanged with time, we may express ψ  as a product of two functions, one of the space coordinates and the other as a function of time.

ψ = f(θ,ϕ,r) f(t)