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A certain pitcher's fastballs have been clocked at about 100 mph. (a) Calculate the wavelength of a \(0.141-\mathrm{kg}\) baseball (in \(\mathrm{nm}\) ) at this speed. (b) What is the wavelength of a hydrogen atom at the same speed? \((1 \mathrm{mile}=1609 \mathrm{~m} .)\)

When light of frequency equal to \(2.11 \times 10^{15} \mathrm{~s}^{-1}\) shines on the surface of gold metal, the kinetic energy of ejected electrons is found to be \(5.83 \times 10^{-19} \mathrm{~J}\) What is the work function of gold?

All molecules undergo vibrational motions. Quantum mechanical treatment shows that the vibrational energy, \(E_{\mathrm{vib}},\) of a diatomic molecule like \(\mathrm{HCl}\) is given by \(E_{\mathrm{vib}}=\left(n+\frac{1}{2}\right) h \nu\) where \(n\) is a quantum given by \(n=0,1,2,3, \ldots\) and \(\nu\) is the fundamental frequency of vibration. (a) Sketch the first three vibrational energy levels for HCl. (b) Calculate the energy required to excite a \(\mathrm{HCl}\) molecule from the ground level to the first excited level. The fundamental frequency of vibration for \(\mathrm{HCl}\) is \(8.66 \times 10^{13} \mathrm{~s}^{-1} .\) (c) The fact that the lowest vibrational energy in the ground level is not zero but equal to \(\frac{1}{2} h \nu\) means that molecules will vibrate at all temperatures, including the absolute zero. Use the Heisenberg uncertainty principle to justify this prediction. (Hint: Consider a nonvibrating molecule and predict the uncertainty in the momentum and hence the uncertainty in the position.

The retina of a human eye can detect light when radiant energy incident on it is at least \(4.0 \times 10^{-17} \mathrm{~J}\). For light of 600 -nm wavelength, how many photons does this correspond to?

The ground-state electron configurations listed here are incorrect. Explain what mistakes have been made in each and write the correct electron configurations. Al: \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{2} 3 p^{3}\) B: \(1 s^{2} 2 s^{2} 2 p^{5}\) \(\mathrm{F}: 1 s^{2} 2 s^{2} 2 p^{6}\)