Show that angular momentum is due to transverse component and does not depend on the radial component i.e. `L = rp_theta`

Show that torque is due to transverse component only and does not depend on the radial component.

Show that the angular momentum is the product of linear momentum and bot distance from the axis of rotation (lever arm) i.e. L = p.d

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null-point (i.e., 14 cm) from the centre of the magnet? (At null points, field due to a magnet is equal and opposite to the horizontal component of earth’s magnetic field.)

Find the components along the x, y, z axes of the angular momentum 1 of a particle, whose position vector is r with components x, y, z and momentum is p with components p_x,p_yand p_z . Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.

True or False Chloroplast is differentiated into two structural components i.e. grana and stroma.

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

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vec L = L = vec L + vecM R xx vecV where vec L = Sigma vecr_i xx vecp_i is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_i = vecr_i - vecR , rest f the notation is the standard notation used in the chapter. Note vecL and vecMR xx vecV can be said to be angular moemnta respectively about and of the centre of mass of the system of particles.

If hydrogen atoms (in the ground state ) are passed through an homogeneous magnetic field, the beam is split into two parts. This interaction with the magnetic field shows that the atoms must have magnetic moment. However, the moment cannot be due to the orbital angular momentum since l=0. Hence one must assume existence of intrinsic angular momentum, which as the experiment shows, has only two permitted orientations. Spin of the electron produce 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 electrons. The substance which contain species with unpaired electrons in their orbitals behave as paramagnetic substances. The paramagnetism is expressed in terms of magnetic moment. The magnetic moment of an atom mu_(s)sqrt(s(s+1))(eh)/(2pimc)=sqrt((n)/(2)((n)/(2)+1))(eh)/(2pimc)" "s=(n)/(2) impliesmu_(s)=sqrt(n(n+1)) B.M. 1. B.M. (Bohr magneton)= (eh)/(4pimc) If magnetic moment is zero the substance is diamagnetic. If an ion of _(25)Mn has a magnetic moment of 3.873 B.M. Then oxidation state of Mn in ion is :

If hydrogen atoms (in the ground state ) are passed through an homogeneous magnetic field, the beam is split into two parts. This interaction with the magnetic field shows that the atoms must have magnetic moment. However, the moment cannot be due to the orbital angular momentum since l=0. Hence one must assume existence of intrinsic angular momentum, which as the experiment shows, has only two permitted orientations. Spin of the electron produce 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 electrons. The substance which contain species with unpaired electrons in their orbitals behave as paramagnetic substances. The paramagnetism is expressed in terms of magnetic moment. The magnetic moment of an atom mu_(s)sqrt(s(s+1))(eh)/(2pimc)=sqrt((n)/(2)((n)/(2)+1))(eh)/(2pimc)" "s=(n)/(2) impliesmu_(s)=sqrt(n(n+1)) B.M. 1. B.M. (Bohr magneton)= (eh)/(4pimc) If magnetic moment is zero the substance is diamagnetic. Which of the following ion has lowest magnetic moment?