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Concept explainers
The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is
(a) What is the probability of finding the electron inside a sphere of volume
(b) What is the probability of finding the electron in a volume of
(c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?
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Chapter 5 Solutions
Principles of Modern Chemistry
- (a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 5.2) to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.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• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.arrow_forward
- For hydrogen atoms, the wave function for the state n = 3, l = 0, ml = 0 is 300=1813(1a0)3/2(2718+22)e where = r/a0 and a0 is the Bohr radius (5.29 1011 m). Calculate the position of the nodes for this wave function.arrow_forwardThe Lyman series of spectral lines for the H atom, in the ultraviolet region, arises from transitions from higher levels to n = 1. Calculate the frequency and wavelength of the least energetic line in this series.arrow_forwardWhich of the following is a valid set of quantum numbers for an electron in a hydrogen atom? (a) n = 1, = 0, m = 0, ms = 1 (b) n = 1, = 1, m = 0, ms = 1/2 (c) n = 1, = 0, m = 1, ms = + 1/2 (d) n = 1, = 0, m = 0, ms = 1/2arrow_forward
- What experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?arrow_forwardUse the mathematical expression for the 2pz wave function of a one-electron atom (see Table 5.2) to show that the probability of finding an electron in that orbital anywhere in the x-y plane is 0. What are the nodal planes for a dxz orbital and for a dx2y2 orbital?arrow_forwardThe ionization energy of rubidium is 403 kJ/mol. Do x-rays with a wavelength of 85 nm have sufficient energy to ionize rubidium?arrow_forward
- This laser emits green light with a wavelength of 533 nm. (a) What is the energy, in joules, of one photon of light at this wavelength? (b) If a particular laser produces 1.00 watt (W) of power (1 W = 1 J/s), how many photons are produced each second by the laser?arrow_forwardWhy is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?arrow_forward6.17 The laser in most supermarket barcode scanners operates at a wavelength of 632.8 nm. What is the energy of a single photon emitted by such a laser? What is the energy of one mole of these photons?arrow_forward
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