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Chapter 6: Problem 96
Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.
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Sodium metal requires a photon with a minimum energy of \(4.41 \times 10^{-19} \mathrm{~J}\) to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect? (b) What is the wavelength of this light? (c) If sodium is irradiated with light of \(405 \mathrm{nm},\) what is the maximum possible kinetic energy of the emitted electrons? (d) What is the maximum number of electrons that can be freed by a burst of light whose total energy is \(1.00 \mu \mathrm{J}\) ?
What is the maximum number of electrons in an atom that can have the following quantum numbers: (a) \(n=2\), \(m_{s}=-\frac{1}{2},\) (b) \(n=5, l=3 ;\) (c) \(n=4, l=3, m_{l}=-3\) (d) \(n=4, l=0, m_{l}=0 ?\)
(a) Why does the Bohr model of the hydrogen atom violate the uncertainty principle? (b) In what way is the description of the electron using a wave function consistent with de Broglie's hypothesis? (c) What is meant by the term probability density? Given the wave function, how do we find the probability density at a certain point in space?
A stellar object is emitting radiation at \(3.55 \mathrm{~mm}\). (a) What type of electromagnetic spectrum is this radiation? (b) If a detector is capturing \(3.2 \times 10^{8}\) photons per second at this wavelength, what is the total energy of the photons detected in one hour?
The following electron configurations represent excited states. Identify the element, and write its ground-state condensed electron configuration. (a) \(1 s^{2} 2 s^{2} 3 p^{2} 4 p^{1},\) (b) \([\mathrm{Ar}] 3 d^{10} 4 s^{1} 4 p^{4} 5 s^{1}\), (c) \([\mathrm{Kr}] 4 d^{6} 5 s^{2} 5 p^{1}\) (a) Determine which elements emit radiation in the visible part of the spectrum. (b) Which element emits photons of highest energy? Of lowest energy? (c) When burned, a sample of an unknown substance is found to emit light of frequency \(6.59 \times 10^{14} \mathrm{~s}^{-1}\). Which of these elements is probably in the sample?
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