4. The red light from a helium-neon laser has a wavelength of 633 nm. What is the energy of one photon? For one mole of these photons? rr ce #3 2$ & 4. t y 8
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- Estimate the probability of finding an electron which is excited into the 2s orbital of the H atom, looking in a cubical box of volume 0.751036m3 centered at the nucleus. Then estimate the probability of finding the electron if you move the volume searched to a distance of 105.8 pm from the nucleus in the positive z direction. (Note that since these volumes are small, it does not matter whether the volume searched is cubical or spherical.)Consider 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).In a FranckHertz experiment on sodium atoms, the first excitation threshold occurs at 2.103 eV. Calculate the wavelength of emitted light expected just above this threshold. (Note: Sodium vapor lamps used in street lighting emit spectral lines with wavelengths 5891.8 and 5889.9 Å.)
- The power output of a laser is measured by its wattage, that is, the number of joules of energy it radiates per second (1W=1Js1) . A 10-W laser produces a beam of green light with a wavelength of 520 nm (5.2107m) . (a) Calculate the energy carried by each photon. (b) Calculate the number of photons emitted by the laser per second.The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr’s quantization of angular momentum to the revolution of Earth (mass6.01024kg) , which moves with a speed of 3.0104ms1 in a circular orbit (radius1.51011m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earthsun system. What would be the effect of an increase in n by 1?Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is 1460 nm. What is the initial excited state for the electron (n = ?)?
- Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a length near 1.34 Å. The motion of an electron in such a bond can be treated crudely as motion in a one-dimensional box. Calculate the energy of an electron in each of its three lowest allowed states if it is confined to move in a one-dimensional box of length 1.34 Å. Calculate the wavelength of light necessary to excite the electron from its ground state to the first excited state.The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (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?In two-photon ionization spectroscopy, the combined energies carried by two different photons are used to remove an electron from an atom or molecule. In such an experiment, a K atom in the gas phase is to be ionized by two different light beams, one of which has a 650-nm wavelength. What is the maximum wavelength for the second beam that will cause two-photon ionization?
- For the Li atom, the energy difference between the ground state and the first excited state, in which the outermost electron is in a 2p orbital, is 2.961019J . In the Li2+ ion, the energy difference between the 2s and 2p levels is less than 0.00002 of this value. Explain this observation.(a) Using Equation 4.36, make a graph of the n=3 wave function and the square of this wave function for a particle in a box with the edges at x=0 and x=7 . Estimate the probability of finding the particle between x1=3 and x2=4 . You may either do an integral or find the area under the curve by counting the number of rectangular boxes (roughly estimating the fractional boxes), and then multiply by the area of each box, watching your units. Show your calculation with units for credit. (b) Verify that the n=3 wave function in (a) is an allowed quantum state (sometimes called an eigenfunction) of by substituting it for in the left side of the equation =E immediately following Eq. 4.32. Calculate the derivatives to see if your result E is a constant multiplied by the original n=3 wavefunction. What does the constant you get tell you about the energy of thiseigenstate? Is it in agreement with the energy for the n=3 level you would calculate from Equation 4.37?When metallic sodium is dissolved in liquid sodium chloride, electrons are released into the liquid. These dissolved electrons absorb light with a wavelength near 800 nm. Suppose we treat the positive ions surrounding an electron crudely as defining a three-dimensional cubic box of edge L, and we assume that the absorbed light excites the electron from its ground state to the first excited state. Calculate the edge length L in this simple model.