Concept explainers
Photoelectron spectroscopy studies of silicon atoms excited by X-rays with wavelength
(a) Calculate the ionization energy of the electrons in each peak.
(b) Assign each peak to an orbital of the silicon atom.
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Principles of Modern Chemistry
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- What is (a) the energy. (b) the speed of an electron that has been ejected from an orbital of ionization energy 10.0 eV by a photon of radiation of wavelength 110 nm?arrow_forwardWhich of the following transitions between terms are allowed in the electronic emission spectrum of a many-electron atom: (i) 3D2 → 3P1, (ii) 3P2 → 1S0, (iii) 3F4 → 3D3?arrow_forward(a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these same two directions for tungsten. (a) [110]: i [111]: i atom/R atom/Rarrow_forward
- The electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using n?h? En 8mlz п 3 1,2, 3, ... where L is the length of the 1D chain. Assuming L = ao(N – 1), where N is the number of Na atoms and ao = 0.360 nm is the internuclear distance. a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enough b) Thermal energy at room temperature is 4.15 × 10-21 J. Calculate the minimum number of Na atoms required so that the energy gap is smaller than the thermal energy.arrow_forwardSingly-ionized carbon atoms are accelerated through 1050 V and passed into a mass spectrometer to determine the isotopes present. The magnetic field strength in the spectrometer is 0.180 T. (a) Determine the orbital radii for the 12C and 13C isotopes as they pass through the field. cm (12C) cm (13C) (b) Show that the ratio of the radii may be written in the form m1 = V by verifying that your radii in part (a) satisfy this formula. m1 m-arrow_forwardThe electronic spectrum of the molecule butadiene, H2C=CH–CH=CH2, can be approximated using the one-dimensional particle-in-a-box if one assumes that the conjugated double bonds span the entire four-carbon chain. If the electron absorbing a photon having wavelength 217 nm is going from the level n =2 to the level n =3, what is the approximate length of the C4H6 molecule?arrow_forward
- Calculate the energy required for a transition from nx = ny = n, = 1 to n, = ny = 1, n, = 2 for an electron in a cubic hole of a crystal having edge length = 1Å %3Darrow_forwardalthough we associate Pz 2. Now we will move on to diatomic molecules. In atoms all p-orbitals are equivalent with m/= 0, and px py with m/= ±1. In diatomic molecules these orbitals are in fact separated, with pz associated with o orbitals along the internuclear axis and px py associated with л orbitals (m/= ±1). In determining electron configurations we do indeed separate them: N₂ (KK¹ 0₂²). and O2 (KKogu ng *2). 4 a. Two excited states of N₂ are associated with Tu transitions. Tg and og → ou* i. Draw the MO energy level scheme (p-orbitals only) for the N₂ ground state and for these two excited states. ii. Obtain the term symbols for the two excited states and order them according to Hund's rules. iii. Write the wave functions for each of the terms obtained in ii) above. iv. Pick one wave function from each excited state and show it obeys the Pauli Principle.arrow_forwardWhen β-carotene is oxidized in vivo, it breaks in half and forms two molecules of retinal (vitamin A), which is a precursor to the pigment in the retina responsible for vision. The conjugated system of retinal consists of 11 C atoms and 1 O atom. In the ground state of retinal, each level up to n = 6 is occupied by two electrons. Assuming an average internuclear distance of 140 pm, calculate (a) the separation in energy between the ground and first exciteted state in which one electron occupies the state with n = 7, and (b) the frequency of radiation required to produce a transition between these two states. From your results, correct the following sentence (from the options in brackets). The absorption spectrum of a linear polyene shifts to (higher/lower) frequency as the number of conjugated atoms (increases/decreases).arrow_forward
- Chemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning