Consider a spin 1/2 particle with spin up along the direction specified by the unit vector n = cos x + sin y. (This vector is in the xy plane and makes an ~ angle with the +x axis.) A spin 1/2 particle with spin up along the n axis is described by the state |+n>= (1/ √2) |+z> + (1/ √2) e° |-z>. Now imagine a beam of spin 1/2 particles traveling along the +z axis. The beam passes through a sequence of three Stern-Gerlach devices. The first one, an SGX device, lets through only particles with Sx=h/2, in other words, with spin up along the x axis. The second device is an SGn device, with its magnetic field oriented along the n axis, and it lets through only particles with spin up along the n axis. The third device, an SGy device, lets through only those particles with spin up along the y axis. (a) Of the particles that get through the first device, what fraction of them get through the last device? (Note how this is worded!) (b) If the middle (SGn) device is removed, what fraction of the particles that get through the first device will get through the last device?

Check Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in the region O and L. One possible wave function is (x,t)={AeiEt/hsinxL, when 0xL otherwise Determine the normalization constant.

Write the election configuration for iron.

Write an expression for the total number of states with orbital angular momentum l.

The valence election of potassium is excited to a 5d state, (a) What is the magnitude of the election's orbital angular momentum? (b) How many states are possible along a chosen direction?

For a 3d electron in an external magnetic field of 2.50 × 10-3 T, find (a) the current associated with the orbital angular momentum, and (b) the maximum torque.

Assume that a proton in a nucleus can be treated as if it were confined to a one-dimensional of width 10.0 fm. (a) What are the energies of the proton when it is in the states corresponding to n=1,n=2, and n=3? (b) What are the energies of the photons emitted when the proton makes the transitions from the first and second excited states to the ground state?

Consider the original Stern–Gerlach experiment employing an atomic beam of silver, for which the magnetic moment is due entirely to the spin of the single valence electron of the silver atom. Assuming the magnetic field B has magnitude 0.500 T, compute the energy difference in electron volts of the silver atoms in the two exiting beams.

Check Your Understanding The vibrational frequency of the hydrogen iodide HI diatomic molecule is 6.691013Hz. (a) What is the force constant of the molecular bond between the hydrogen and the Iodine atoms? (b) What is the energy of the emitted photon when this molecule makes a transition between adjacent vibration energy levels?

Check Your Understanding Can the magnitude of Lzever be equal to L?