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Chapter 41: Q. 6 (page 1206)

Does each of the configurations in FIGURE Q41.6represent a possible electron configuration of an element? If so,

(i) identify the element and

(ii) determine whether this is the ground state or an excited state. If not, why not?

Short Answer

Expert verified

2pa. Yes, this is the ground state of nitrogen. The psubshells have 6states, then they can accept three electrons without the Pauli exclusion principle.

b. No, the only two electrons are accessed in the 2sstate.

c. No, the 2sstates are the lowest energy than the 2pstates, then the ground state would be occupied before the 2pstate.

Step by step solution

01

Part (a) step 1: Given Information 

We need to find identify the element and determine whether this is the ground state or an excited state in diagram (a).

02

Part (a) step 2: Explanation

Yes, this is the ground state of nitrogen. The psubshells have 6states, then they can accept three electrons without the Pauli exclusion principle.

03

Part (b) step 1: Given Information 

We need to find identify the element and determine whether this is the ground state or an excited state in diagram (b).

04

Part (b) step 2: Explanation

No, the only two electrons are accessed in the 2sstate.

05

Part (c) step 1: Given Information 

We need to find identify the element and determine whether this is the ground state or an excited state in diagram (c).

06

Part (c) step 2: Explanation

No, the 2sstates are the lowest energy than the 2pstates, then the ground state would be occupied before the 2pstate.

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Most popular questions from this chapter

The 1997Nobel Prize in physics went to Steven Chu, Claude Cohen-Tannoudji, and William Phillips for their development of techniques to slow, stop, and “trap” atoms with laser light. To see how this works, consider a beam of rubidium atoms mass1.4×10-25kg traveling at 500m/safter being evaporated out of an oven. A laser beam with a wavelength of 780nm is directed against the atoms. This is the wavelength of the 5s→5ptransition in rubidium, with 5s being the ground state, so the photons in the laser beam are easily absorbed by the atoms. After an average time of 15ns, an excited atom spontaneously emits a 780nmwavelength photon and returns to the ground state.

a. The energy-momentum-mass relationship of Einstein’s theory of relativity is E2=p2c2+m2c4. A photon is massless, so the momentum of a photon is p=Ephoton/c. Assume that the atoms are traveling in the positive x-direction and the laser beam in the negative x-direction. What is the initial momentum of an atom leaving the oven? What is the momentum of a photon of light?

b.The total momentum of the atom and the photon must be conserved in the absorption processes. As a consequence, how many photons must be absorbed to bring the atom to a halt?

NOTE Momentum is also conserved in the emission processes. However, spontaneously emitted photons are emitted in random directions. Averaged over many absorption/emission cycles, the net recoil of the atom due to emission is zero and can be ignored.

c. Assume that the laser beam is so intense that a ground-state atom absorbs a photon instantly. How much time is required to stop the atoms?

d. Use Newton’s second law in the form F=∆p/∆tto calculate the force exerted on the atoms by the photons. From this, calculate the atoms’ acceleration as they slow.

e. Over what distance is the beam of atoms brought to a halt?

An atom in an excited state has a1.0% chance of emitting a photon in 0.20ns. How long will it take for 25%of a sample of excited atoms to decay?

Three electrons are in a one-dimensional rigid box (i.e., an infinite potential well) of length 0.50nm. Two are in the n = 1 state and one is in the n = 6 state. The selection rule for the rigid box allows only those transitions for which n is odd.

a. Draw an energy-level diagram. On it, show the filled levels and show all transitions that could emit a photon.

b. What are all the possible wavelengths that could be emitted by this system?

a. Draw a diagram similar to Figure 41.2 to show all the possible orientations of the angular momentum vector L→for the case l=3. Label each L→with the appropriate value of m.

b. What is the minimum angle between L→and the z-axis?

A 1.0mW helium-neon laser emits a visible laser beam with a wavelength of 633nm. How many photons are emitted per second?

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