(a) The nitrogen atom has one electron in each of the
(b) The same result as in part (a) applies to d orbitals, thus a filled or half-filled subshell of d orbitals is spherically symmetric. Identify the spherically symmetric atoms or ions among the following:
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Chapter 5 Solutions
Principles of Modern Chemistry
- A nonmetallic element, R, burns brightly in air to give the oxide R4O10. If R is in Period 3, what is the ground-state valence-shell configuration of the atom?arrow_forward• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.arrow_forwardConsider burning ethane gas, C2H6 in oxygen (combustion) forming CO2 and water. (a) How much energy (in J) is produced in the combustion of one molecule of ethane? (b) What is the energy of a photon of ultraviolet light with a wavelength of 12.6 nm? (c) Compare your answers for (a) and (b).arrow_forward
- Spectroscopists have observed He+ in outer space. This ion is a one-electron species like a neutral hydrogen atom. Calculate the energy of the photon emitted for the transition from the n = 5 to the n = 3 state in this ion using the equation: En = − Z2/n2 (2.179 × 10−18 J). Z is the positive charge of the nucleus and n is the principal quantum number. In what part of the electromagnetic spectrum does this radiation lie?arrow_forwardWhat is the electron configuration of the Ba3+ ion? Suggest a reason why this ion is not normally found in nature.arrow_forwardA hydrogen atom consists of a proton and an electron. According to the Bohr theory, the electron revolves about the proton in a circle of radius a (a = 5 · 10−9cm for the ground state). According to quantum mechanics, the electron may be at any distance r (from 0 to ∞) from the proton; for the ground state, the probability that the electron is in a volume element dV , at a distance r to r + dr from the proton, is proportional to e−2r/adV , where a is the Bohr radius. Write dV in spherical coordinates (see Chapter 5, Section 4) and find the density function f(r) so that f(r) dr is the probability that the electron is at a distance between r and r + drfrom the proton. (Remember that the probability for the electron to be somewhere must be 1.) Computer plot f(r) and show that its maximum value is at r = a; we then say that the most probable value of r is a. Also show that the average value of r−1 is a−1.arrow_forward
- Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons arecaptured by an atom, they orbit just like an electron but with a smaller radius, since the mass in aB =0.529x 10-10 m is 207 me .(a) Calculate the radius of the n=1 orbit for a muon in a uranium ion( Z=92).(b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can seethat the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.arrow_forward(ii) The probability of finding an electron at a certain point in an orbital increases proportional to r 2. Explain why this might be.arrow_forwardPhotoelectron spectroscopy applies the principle of the pho-toelectric effect to study orbital energies of atoms and mol-ecules. High-energy radiation (usually UV or x-ray) is absorbedby a sample and an electron is ejected. The orbital energy can becalculated from the known energy of the radiation and the mea-sured energy of the electron lost. The following energy differ-ences were determined for several electron transitions:ΔE 2→1=4.098X10⁻¹⁷J, ΔE 3→1=4.854X10⁻¹⁷J, ΔE 5→1=5.242X10⁻¹⁷J, ΔE 4→2=1.024X10⁻¹⁷J Calculate the energy change and the wavelength of a photon emitted in the following transitions:(a) Level 3→2 (b) Level4→1 (c) Level5→4arrow_forward
- A beryllium ion with a single electron (denoted Be3+ ) is in an excited state with radius the same as that of the ground state of hydrogen. (a) What is n for the Be3+ ion? (b) How much energy in eV is needed to ionize the ion from this excited state?arrow_forwardWhen ultraviolet radiation of wavelength 58.4 nm from a helium lamp is directed on to a sample of krypton, electrons are ejected with a speed of 1.59 x 106 m s-1. Calculate the ionization energy of krypton.arrow_forwardhv=1E+ 1/2mu2 where v is the frequency of the UV light,and m and u are the mass and velocity of the electron, respectively. In one experiment the kinetic energy of the ejected electron from potassium is found to be 5.34 x 10-19 ] using a UV source of wavelength 162 nm. Calculate the ionization energy of potassium. How can you be sure that this ionization energy corresponds to the electron in the valence shell (that is, the most loosely held electron)?arrow_forward
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