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FIGUREP41.41shows the first few energy levels of the lithium atom. Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicate

a. The wavelength, in nm.

b. Whether the transition is in the infrared, the visible, or the ultraviolet spectral region.

c. Whether or not the transition would be observed in the lithium absorption spectrum.


Short Answer

Expert verified

a) For transition wavelength is shown in nm.

b) Whether the transition is in the infrared, the visible, or the ultraviolet spectral region, it is shown in table.

c )In the table ,it is shown whether or not the transition would be observed in the lithium absorption spectrum.

Step by step solution

01

Part(a)Step 1 : Given information

We are given FIGUREP41.41shows the first few energy levels of the lithium atom .

We need to Make a table showing all the allowed transitions in the emission spectrum indicating wavelength, whether the transition is in the infrared, the visible, or the ultraviolet spectral region, whether or not the transition would be observed in the lithium absorption spectrum .

02

Part(a)Step 2 : Explanation 

Formula used will be , E=hc=1240eVnm

Transition a) Wavelength(nm) localid="1650734260872" 2p2s670nm3s2p816nm3p2s324nm3p3s2696nm3d2p611nm3d3p24.800nm4s2p498nm4s3p2430nm

03

Part(b)Step 1 : Given information

We are given that FIGUREP41.41shows the first few energy levels of the lithium atom .

We need to Make a table showing all the allowed transitions in the emission spectrum indicating wavelength, whether the transition is in the infrared, the visible, or the ultraviolet spectral region, whether or not the transition would be observed in the lithium absorption spectrum .

04

Part(b)Step 2 : Explanation 

We will use relation between energy and wavelength, E=hc=1240eVnm

Transition b)Type ( )

localid="1650734358113" 2p2sVIS3s2pIR3p2sUV3p3sIR3d2pVIS3d3pIR4s2pVIS4s3pIR

05

Part(c)Step 1 : Given information

We are given that FIGUREP41.41shows the first few energy levels of the lithium atom .

We need to Make a table showing all the allowed transitions in the emission spectrum indicating wavelength, whether the transition is in the infrared, the visible, or the ultraviolet spectral region, whether or not the transition would be observed in the lithium absorption spectrum .

06

Part(c)Step 2 : Explanation 

We will use relation between energy and wavelength, E=hc=1240eVnm

Transition c)Absorption

2p2sYes3s2pNo3p2sYes3p3sNo3d2pNo3d3pNo4s2pNo4s3pNo

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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 鈥渢rap鈥 atoms with laser light. To see how this works, consider a beam of rubidium atoms mass1.410-25kg 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 5s5ptransition 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鈥檚 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鈥檚 second law in the form F=p/tto calculate the force exerted on the atoms by the photons. From this, calculate the atoms鈥 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?

What is the maximum possible angular momentumL(as a multiple of h) of a hydrogen atom with energy-0.544eV?

An excited state of an atom has a 25nslifetime. What is the probability that an excited atom will emit a photon during a 0.50ns interval?

Two excited energy levels are separated by the very small energy difference E. As atoms in these levels undergo quantum jumps to the ground state, the photons they emit have nearly identical wavelengths .

a. Show that the wavelengths differ by

=2hcE

b. In the Lyman series of hydrogen, what is the wavelength difference between photons emitted in the n=20to n=1transition and photons emitted in the n=21to n=1transition?

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