The magnetic moment vectors `mu_(s) and mu_(l)` associated with the intrinsie spin angular momentum S and orbital angular momentum l, respectively, of an electron are predicted by quantum theory (and verified expenmentally to a high accuracy) to be given by:
`mu_(s)=-(e//m) S,`
`mu_(1)=-(e//2m)l`
Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

Spin angular momentum of an electron has no analog in classical mechanics. However, it turns out that the treatment of spin angular momentum is closely analogous to the treatment of orbital angular momentum. Spin angular momentum = sqrt(s(s+1)h) Orbital angular momentum = sqrt(l(l+1)h) Total spin of an atom or ion is a multiple of (1)/(2) . Spin multiplicity is a factor to confirm the electronic configuration of an atom or ion. Spin multiplicity (2 sum s +1) The orbital angular momentum for a 2p-electron is :

Spin angular momentum of an electron has no analog in classical mechanics. However, it turns out that the treatment of spin angular momentum is closely analogous to the treatment of orbital angular momentum. Spin angular momentum = sqrt(s(s+1)h) Orbital angular momentum = sqrt(l(l+1)h) Total spin of an atom or ion is a multiple of (1)/(2) . Spin multiplicity is a factor to confirm the electronic configuration of an atom or ion. Spin multiplicity (2 sum s +1) In any subshell, the maximum number of electrons having same value of spin quantum number is :

Assertion (A) : The orbital angular momentum of 2s-electron is equal to that of 3s-electron. Reason (R) : The orbital angular momentum is given by the relation sqrt(l(l+1))(h)/(2pi) and the value of 1 is same for 2s-electron and 3s-electron.

Spin angular momentum of an electron has no analog in classical mechanics. However, it turns out that the treatment of spin angular momentum is closely analogous to the treatment of orbital angular momentum. Spin angular momentum = sqrt(s(s+1)h) Orbital angular momentum = sqrt(l(l+1)h) Total spin of an atom or ion is a multiple of (1)/(2) . Spin multiplicity is a factor to confirm the electronic configuration of an atom or ion. Spin multiplicity (2 sum s +1) Total spin of Mn^(2+) = (Z = 25) ion will be :

Just as Bohr.s model of atom was developed on the basis of planck.s quantum theory, wave mechanical model of atom has been developed on the basis of quantum mechanics. The herat of quantum mechanism is Schrodinger wave equation which in turn is based on Heisenberg.s uncetainity principle and de broglie concept of dual nature of matter and radiation. Bohr model could explain the main lines of hydrogen or hydrogenic spectra but could not explain their fine structure. To explain this, it was suggested that each level consists of a number of sublevels, it was suggested that each level consists of a number of sublevels, the transitions between which gave rise to closely spaced lines. The numbers representing the main energy level are called Princiapl Quantum Number (n) while those representing sublevels are called Azimuthal Quantum numbers (l) and these determine the angular momentum of the electron. The orbital angular Number (m) which is just like a further split of a sublevel into finer sublevels. Lastly the electron may rotate or spin about its own axis given rise to Spin Quantum number (s) which determines the angular momentum of the electron. The de Broglie wavelength (lambda) of the electron subjected to an accelerating potential of V volts is given by

In the Bohr atom model the electrons move around the nucleus in circular orbits. Obtain an expression the magnetic moment (mu) of the electron in a Hydrogen atom in terms of its angular momentum L.

It is tempting to think that all possible transitions are permissible, and that an atomic spectrum arises from the transition of the electron from any initial orbital to any other orbital. However, this is not so, because a photon has an intrinsic spin angular momentum of sqrt2 (h)/(2pi) corresponding to S = 1 although it has no charge and no rest mass. On the other hand, an electron has got two types of angular momentum : Orbital angular momentum, L=sqrt(l(l+1))h/(2pi) and spin angular momentum, arising from orbital motion and spin motion of electron respectively. The change in angular momentum of the electron during any electronic transition mush compensate for the angular momentum carries away by the photon. to satisfy this condition the difference between the azimuthal quantum numbers of the orbital within which transition takes place must differ by one. Thus, an electron in a d-orbital (1 = 2) cannot make a transition into an s = orbital (I = 0) because the photon cannot carry away enough angular momentum. An electron as is well known, possess four quantum numbers n, I, m and s. Out of these four I determines the magnitude of orbital angular momentum (mentioned above) while (2n m determines its z-components as m((h)/(2pi)) the permissible values of only integers right from -1 to + l. While those for I are also integers starting from 0 to (n − 1). The values of I denotes the sub shell. For I = 0, 1, 2, 3, 4,..... the sub-shells are denoted by the symbols s, p, d, f, g, .... respectively The spin-only magnetic moment of free ion is sqrt(8) B.M. The spin angular momentum of electron will be

It is tempting to think that all possible transitions are permissible, and that an atomic spectrum arises from the transition of the electron from any initial orbital to any other orbital. However, this is not so, because a photon has an intrinsic spin angular momentum of sqrt2 (h)/(2pi) corresponding to S = 1 although it has no charge and no rest mass. On the other hand, an electron has got two types of angular momentum : Orbital angular momentum, L=sqrt(l(l+1))h/(2pi) and spin angular momentum, 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 carries away by the photon. to satisfy this condition the difference between the azimuthal quantum numbers of the orbital within which transition takes place must differ by one. Thus, an electron in a d-orbital (1 = 2) cannot make a transition into an s = orbital (I = 0) because the photon cannot carry away enough angular momentum. An electron as is well known, possess four quantum numbers n, I, m and s. Out of these four I determines the magnitude of orbital angular momentum (mentioned above) while (2n m determines its z-components as m((h)/(2pi)) the permissible values of only integers right from -1 to + l. While those for I are also integers starting from 0 to (n − 1). The values of I denotes the sub shell. For I = 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 election is :

It is tempting to think that all possible transitions are permissible, and that an atomic spectrum arises from the transition of the electron from any initial orbital to any other orbital. However, this is not so, because a photon has an intrinsic spin angular momentum of sqrt2 (h)/(2pi) corresponding to S = 1 although it has no charge and no rest mass. On the other hand, an electron has got two types of angular momentum : Orbital angular momentum, L=sqrt(l(l+1))h/(2pi) and spin angular momentum, 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 carries away by the photon. to satisfy this condition the difference between the azimuthal quantum numbers of the orbital within which transition takes place must differ by one. Thus, an electron in a d-orbital (1 = 2) cannot make a transition into an s = orbital (I = 0) because the photon cannot carry away enough angular momentum. An electron as is well known, possess four quantum numbers n, I, m and s. Out of these four I determines the magnitude of orbital angular momentum (mentioned above) while (2n m determines its z-components as m((h)/(2pi)) he permissible values of only integers right from -1 to + l. While those for I are also integers starting from 0 to (n − 1). The values of I denotes the sub shell. For I = 0, 1, 2, 3, 4,..... the sub-shells are denoted by the symbols s, p, d, f, g, .... respectively The maximum orbital angular momentum of an electron with n= 5 is

Just as Bohr.s model of atom was developed on the basis of planck.s quantum theory, wave mechanical model of atom has been developed on the basis of quantum mechanics. The herat of quantum mechanism is Schrodinger wave equation which in turn is based on Heisenberg.s uncetainity principle and de broglie concept of dual nature of matter and radiation. Bohr model could explain the main lines of hydrogen or hydrogenic spectra but could not explain their fine structure. To explain this, it was suggested that each level consists of a number of sublevels, it was suggested that each level consists of a number of sublevels, the transitions between which gave rise to closely spaced lines. The numbers representing the main energy level are called Princiapl Quantum Number (n) while those representing sublevels are called Azimuthal Quantum numbers (l) and these determine the angular momentum of the electron. The orbital angular Number (m) which is just like a further split of a sublevel into finer sublevels. Lastly the electron may rotate or spin about its own axis given rise to Spin Quantum number (s) which determines the angular momentum of the electron. The quantum number not obtained from the solution of Schrodinger wave equation is