How many different 3d states are there? What physical property (as opposed to quantum number) distinguishes them, and what different values may this property assume?

Short Answer

Expert verified

There are five states in the case of 3d states.

The angular momentum could be 0 or±h or±2h .

Step by step solution

01

Given data

The principal quantum number, n = 3, and the subshell is d.

02

To find different 3d states and angular momentum

The state 3d means principal quantum number n = 3 , the azimuthal quantum number l=n-1=2 so that magnetic quantum number ml, can take values from -l to +l as -2, -1, 0, 1 2.

So, there are five states.

The states that have differentrole="math" localid="1659781123812" ml have different orbits and electron probability densities. They have different angular momentum in the z-direction, that isLz=mih .

The angular momentum could be 0 or±h or±2h .

03

Conclusion

There are five states in the case of 3d states.

The angular momentum could be 0 or±h or±2h

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Most popular questions from this chapter

Consider a cubic 3D infinite well.

(a) How many different wave functions have the same energy as the one for which (nx,ny,nz)=(5,1,1)?

(b) Into how many different energy levels would this level split if the length of one side were increased by 5% ?

(c) Make a scale diagram, similar to Figure 3, illustrating the energy splitting of the previously degenerate wave functions.

(d) Is there any degeneracy left? If so, how might it be “destroyed”?

A comet of 1014kg mass describes a very elliptical orbit about a star of mass3×1030kg , with its minimum orbit radius, known as perihelion, being role="math" localid="1660116418480" 1011m and its maximum, or aphelion, 100 times as far. When at these minimum and maximum

radii, its radius is, of course, not changing, so its radial kinetic energy is 0, and its kinetic energy is entirely rotational. From classical mechanics, rotational energy is given by L22I, where Iis the moment of inertia, which for a “point comet” is simply mr2.

(a) The comet’s speed at perihelion is6.2945×104m/s . Calculate its angular momentum.

(b) Verify that the sum of the gravitational potential energy and rotational energy are equal at perihelion and aphelion. (Remember: Angular momentum is conserved.)

(c) Calculate the sum of the gravitational potential energy and rotational energy when the orbit radius is 50 times perihelion. How do you reconcile your answer with energy conservation?

(d) If the comet had the same total energy but described a circular orbit, at what radius would it orbit, and how would its angular momentum compare with the value of part (a)?

(e) Relate your observations to the division of kinetic energy in hydrogen electron orbits of the same nbut different I.

Consider a 2D infinite well whose sides are of unequal length.

(a) Sketch the probability density as density of shading for the ground state.

(b) There are two likely choices for the next lowest energy. Sketch the probability density and explain how you know that this must be the next lowest energy. (Focus on the qualitative idea, avoiding unnecessary reference to calculations.)

Knowing precisely all components of a nonzero Lwould violate the uncertainty principle, but knowingthat Lis precisely zerodoes not. Why not?

(Hint:For l=0 states, the momentum vector p is radial.)

(a) For one-dimensional particle in a box, what is the meaning of n? Specifically, what does knowing n tell us? (b) What is the meaning of n for a hydrogen atom? (c) For a hydrogen atom. What is the meaning of landml?

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