36. The emission spectrum below for a one-electron (hydrogen-like) species in the gasphase shows all the lines, before they merge together, resulting from transitions to thefirst excited state from higher energy states. Line A has a wavelength of 434 nm.BAIncreasing wavelength, λ(a) What are the upper and lower principal quantum numbers corresponding to the lineslabeled A and B? (b) Identify the one-electron species that exhibits the spectrum.

Answered: Image /qna-images/answer/21ee5d32-3449-4532-b3d5-1c94689ca48a.jpg

Answered: 36. The emission spectrum below for a…

Introductory Chemistry: An Active Learning Approach

6th Edition

ISBN:9781305079250

Author:Mark S. Cracolice, Ed Peters

Publisher:Mark S. Cracolice, Ed Peters

Chapter11: Atomic Theory :the Quantum Model Of The Atom

Section: Chapter Questions

Problem 109E

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When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid. These dissolved electrons absorb light with a wavelength near 800 nm. Suppose we treat the positive ions surrounding an electron crudely as defining a three-dimensional cubic box of edge L, and we assume that the absorbed light excites the electron from its ground state to the first excited state. Calculate the edge length L in this simple model.
Suppose that the spin quantum number did not exist, and therefore only one electron could occupy each orbital of a many-electron atom. Give the atomic numbers of the first three noble-gas atoms in this case.
Until recently, it was thought that Ca was unstable, and that the Ca atom therefore had a negative electron affinity. Some new experiments have now measured an electron affinity of +2.0kJmol1 for calcium. What is the longest wavelength of light that could remove an electron from Ca ? In which region of the electromagnetic spectrum does this light fall?
For the Li atom, the energy difference between the ground state and the first excited state, in which the outermost electron is in a 2p orbital, is 2.961019J . In the Li2+ ion, the energy difference between the 2s and 2p levels is less than 0.00002 of this value. Explain this observation.
Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom, looking in a cubical box of volume 0.751036m3 centered at the nucleus. Then estimate the probability of finding the electron if you move the volume searched to a distance of 105.8 pm from the nucleus in the positive z direction. (Note that since these volumes are small, it does not matter whether the volume searched is cubical or spherical.)
Using Table 5.2, write down the mathematical expression for the 2px wave function for an electronically excited H atom. Estimate the probability of finding the 2px electron if you look in a cubical box of volume of 0.8(pm)3 centered at a distance of 0.5001010m in the =/2 , =0 direction. Does this probability change as you change ? At what angles is the probability of finding the electron smallest and at what angles is the probability the largest? (Note that =2 is the same location as =0 , so don’t double count.)
Construct an energy level diagram showing all orbitals for the hydrogen atom up to n=5, labeling each orbital with its appropriate quantum numbers. How many different orbitals are in each shell?
The figure below represents part of the emission spectrum for a one-electron ion in lhe gas phase. All the lines result from electronic transitions from excited states to the n = 3 state. (See Exercise 160.) a. What electronic transitions correspond to lines A and B? b. If the wavelength of line B is 142.5 nm, calculate the wavelength of line A.
Consider the representations of the p and d atomic orbitals in Figs. 2-15 and 2- 17. What do the + and signs indicate?
The energy needed to ionize an atom of element X when it is in its most stable state is 500kJmol1 . However, if an atom of X is in its lowest excited state, only 120kJmol1 is needed to ionize it. What is the wavelength of the radiation emitted when an atom of X undergoes a transition from the lowest excited state to the ground state?
Cesium is used extensively in photocells and in television cameras because it has the lowest ionization energy of all the stable elements. (a) What is the maximum kinetic energy of a photoelectron ejected from cesium by 520 nm light? Note that if the wavelength of the light used to irradiate the cesium surface becomes longer than 660 nm, no photoelectrons are emitted. (b) Use the rest mass of the electron to calculate the velocity of the photoelectron in (a).
Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.

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