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STATEMENT -1 : Orbital angular momentum ...

STATEMENT -1 `:` Orbital angular momentum is given by `sqrt(l(l+1))(h)/(2pi)`
and
STATEMENT-2 `:` I ( Quantum number ) decides the shape of orbital

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 isTrue, Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False , Statement-2 isTrue

Text Solution

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The orbital angular momentum of a p electron is equal to sqrt(2) (h)/(2pi)

STATEMENT-1 : The orbital angular momentum of an e^(-) in 4f atomic orbital is sqrt( 12) ( h)/( 2pi) and STATEMENT-2 : The orbital angualar momentum of an electron is given by sqrt(l(l+1)) ( h)/( 2pi) and for f-subshell, l=3

For a 'd' electron, the orbital angular momentum is (h =(h)/(2pi))

STATEMENT-1: The angular momentum of d-orbitals is sqrt6(h)/(2pi) STATEMENT 2 : Angular momentum of electron in orbit is mvr=(nh)/(2pi)

When the azimuthal quantum number l = 1, the shape of the orbital will be

Azimuthal quantum number (l): it desiibes the shape of electron cloud and the number of sub- shells in a shell . it can have values from 0 to (n-1) {:("value of l","subshell"),(0,s),(1,p),(2,d),(3,f):} Number of obitals in a subsjhell = 2l +1 Orbital angular momentum L=(h)/(2 pi)sqrt(l(l+1)) hsqrt(l(l+1))" " [h=(h)/(2pi)] magb=netic quantum number (m) : it desicribes the orientations of the orbitals .It can have values from -l to + l including zerop i.e total (2l+1) values . Each value corresponds to an ot=rbital s- subshell has one orbital ,p - subshell three orbitals (P_(x),P_(y)andP_(z)) d- subshell five orbitals (D_(yz),d_(yz),d_(zx), d_(x^(2)-y^(2)),d_(z^(2)) and f- subshelll has seven orbtials . Spin quantum number (s) : It desiibes the spin of the electron , it has values +(1)/(2) and -(1)/(2) Signifies clock wise spining and anticlock wise rotion of electron about its Own axis . Spin of the electron produes spin angluar momentum equal to S=sqrt(s(s+1))(h)/(2pi), "where" s= +(1)/(2) total of the an atom =+(n)/(2) or -(n)/(2) WHere n is the number of unpaired electron s . the magnetic moment of an atom mu_(s)=sqrt(n(n+2))B.M n- number of unpaired electron s B.M (Bohr magenton) orbit angulaar momentum of an electron is sqrt(3) (h)/(pi) then , the number of different orientations of this orbital in space are:

Azimuthal quantum number (l) : It describes the shape of electron cloud and the number of subshells in a shell. It can have value from 0 to (n-1) {:("Value of l",0,1,2,3),("subshell",s,p,d,r):} Number of orbitals in a subshell =2l+1 Orbital angular momentum L =h/(2pi)sqrt(l(l+1)) =ħsqrt(l(l+1)) " " [ħ=h/(2pi)] Magnetic quantum number (m) : It describes the orientations of the subshells . It can have values from -l to +l including zero, i.e. , total (2l+1) values . Each value corresponds to an orbital. s-subshell has one orbital , p-subshell three orbitals (p_x ,p_y and p_z) , d-subshell five orbitals (d_"xy", d_"yz",d_(x^2-y^2), d_z^2) and f-subshell has seven orbitals. Spin quantum number (s) : It describes the spin of the electron. It has values +1/2 and -1/2 . Signifies clockwise spinning and anticlockwise rotation of electron about its own axis. Spin of the electron produces angular momentum equal to S=sqrt(s(s+1)) h/(2pi) where s=+1/2 Total spin of an atom =+n/2 or -n/2 (where n is the number of unpaired electron ) The magnetic moment of an atom mu_s=sqrt(n(n+2)) B.M. n=number of unpaired electrons B.M. (Bohr magneton) Orbital angular momentum of an electron is sqrt3h/pi then the number of orientations of this orbital in spaces are :

It is tempting to think that all possible transitions are permissible, and that an atomic spectrum arises from the transition of an electron from nay initial orbital to any other orbital. However, this is no so, because a photon has an intrinsic spin angular momentum of sqrt(2)(h)/(2pi) corresponding to S = 1 although it has no charge and no rest mass. on the otherhand, an electron has got two types of angular momentum: Orbital angular momentum, L = = sqrt(l(l+1))(h)/(2pi) and spin angular momentum, L_(s) (=sqrt(s(s+1))(h)/(2pi)) arising from orbital motion and spin motion of electron respectively. The change in angular momentum of the electron during any electronic transition must compensate for the angular momentum carried away by the photon. To satisfy this condition the difference between the azimuthal quantum numbers of the orbitals within which transition takes place must differ by one. Thus, an electron in a d-orbital (l=2) cannot make a transition into an s-orbital (l=0) because the photon cannot carry away enough angular momentum. An electron, possess four quantum numbers, n l, m and s. Out of these four l determines the magnitude of orbital angular momentum (mentioned above) while m determines its Z-component as m((h)/(2pi)) . The permissible values of only integers right from -l to +l . While those for l are also integers starting from 0 to (n-1) . The values of l denotes the sub-shell. For l = 0,1,2,3,4... the sub-shells are denoted by the symbols s,p,d,f,g....respectively. The orbital angular momentum of an electron in p-orbital makes an angle of 45^(@) from Z-axis. Hence Z-component of orbital angular momentum of electron is: