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JEE Exam  >  JEE Questions  >  In an orbital motion, the angular momentum ve... Start Learning for Free
In an orbital motion, the angular momentum vector is
  • a)
    in the orbital plane
  • b)
    parallel to linear momentum
  • c)
    along the radius vector
  • d)
    perpendicular to the orbital plane
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In an orbital motion, the angular momentum vector isa)in the orbital p...
Explanation:

Angular momentum is a vector quantity which is defined as the product of the moment of inertia and the angular velocity of a particle. In an orbital motion, the angular momentum vector is given by the cross product of the position vector and the linear momentum vector.

L = r x p

where L is the angular momentum vector, r is the position vector and p is the linear momentum vector.

Now, let's consider the orbital motion of a particle around a central force. In this case, the force acting on the particle is always directed towards the center of the orbit. As a result, the linear momentum vector of the particle is always perpendicular to the position vector, i.e., it lies in the orbital plane.

Therefore, the angular momentum vector of the particle is given by the cross product of two vectors which lie in the orbital plane. Hence, the angular momentum vector is perpendicular to the orbital plane.

Thus, the correct answer is option D, i.e., the angular momentum vector is perpendicular to the orbital plane.
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The orbital and spin angular momentum of the atom influence its magnetic structure and these properties are most directly studied by placing the atom in a magnetic field. Also, a magnetic field can affect the wavelengths of the emitted photons.The angular momentum vector associated with an atomic state can take up only certain specified directions in space. This concept of space quantization was shown by Otto Stern and Walthor Gerlach in their experiment.In the experiment, silver is vapourized in an electric oven and silver atoms spray into the evacuated apparatus through a small hole in the oven wall. The atoms which are electrically neutral but have a magnetic moment, are formed into a narrow beam as they pass through a slit in a screen. The beam, thus collimated, then passes between the poles of an electromagnet and finally, deposits its silver atoms on a glass plate that serves as a detector. The pole faces of the magnet are shaped to make the magnetic field as nonuniform as possible.In a non-uniform magnetic field, there is a net force on a magnetic dipole. Its magnitude and direction depends on the orientation of the dipole. Thus the silver atoms in the beam are deflected up or down, depending on the orientation of their magnetic dipole moments with respect to the z–direction.The potential energy of a magnetic dipole in a magnetic field where is magnetic dipole moment of the atom. From symmetry, the magnetic field at the beam position has no x or y components i.e.The net force Fz on the dipole isThus, the net force depends, not on the magnitude of the field itself, but on its spatial derivative or gradient.The ResultsIf space quantization did not exist, then could take on any value from + to –, the result would be a spreading out of the beam when the magnet was turned ON. However, the beam was split cleanly into two subbeams, each subbeam corresponding to one of the two permitted orientations of the magnetic moment ofthe silver atom, as shown.In a silver atom, all the spin and orbital magnetic moments of the electrons cancel, except for those of the atoms single valance electron. For this electron the orbital magnetic moment is zero because orbital angular momentum is zero (because for electrons of s–orbit, L = 0), leaving only the spin magnetic moment. This can take up only two orientations in a magnetic field, corresponding to ms = +1/2 and ms = – 1/2. Hence there are two subbeams – and not some other number.Q.A hydrogen atom in ground state passes through a magnetic field that has a gradient of 16mT/m in the vertical direction. If vertical component magnetic moment of the atom is 9.3 × 10–24 J/T, then force on it due to the magnetic moment of the electron is

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In an orbital motion, the angular momentum vector isa)in the orbital planeb)parallel to linear momentumc)along the radius vectord)perpendicular to the orbital planeCorrect answer is option 'D'. Can you explain this answer?
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