Fundamentals Of Hydraulic Engineering Systems 4th Edition Robert J. Houghtalen, A. Osman H. Akan, Ned H. C. Hwang - Solutions

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Photons of energy 6.0eV incident on a metal, it is found that current flows from the metal until a stopping potential of 4.0V is applied. If the wavelength of the incident photons is doubled, what is the maximum kinetic energy of the ejected electrons? What would happen if the wavelength of the
Visible light incident on a diffraction grating with slit spacing of 0.010 mm has the first maximum at an angle of 3.5o from the central peak. If electrons could be diffracted by the same grating, what electron velocity would produce the same diffraction pattern as the visible light?
(a) Suppose an unknown element has a absorption spectrum with lines at 2.5, 4, and 5.1eV above its ground state and an ionization energy of 11.5eV. Draw an energy level diagram for this element.(b) If a 5.1-eV photon is absorbed by an atom of this substance, in which state was the atom before
Light of wavelength 424nm falls on a metal which has a work function of 2.28eV(a) How much voltage should be applied to bring the current to zero?(b) What is the maximum speed of the emitted electrons?(c) What is the de Broglie wavelength of these electrons?
An electron accelerated from rest by a 96-V potential difference is injected into a 3.67 x 10–4T magnetic field where it travels in an 18-cm-diameter circle. Calculate e/m from this information.
Estimate the number of photons emitted by the Sun in a year. (Take the average wavelength to be 550 nm and the intensity of sunlight reaching the Earth (outer atmosphere) as 1350W/m2.)
Apply Bohr’s assumption to the Earth-Moon system to calculate the allowed energies and radii of motion. Given the know distance between the Earth and Moon, Is the quantization of the energy and radius apparent?
Compare a matter wave ψ to (a) A wave on a string (b) An Em wave. Discuss similarities and differences.
Explain why Bohr’s theory of the atom is not compatible with quantum mechanics, particularly the uncertainty principle.
In view of the uncertainty principle, why does a baseball seem to have a well-defined position and speed whereas an electron does not?
Explain why it is that the more massive an object is, the casier it becomes to predict its future position.
Would it ever be possible to balance a very sharp needle precisely on its point? Explain.
A cold thermometer is placed in a hot bowl of soup before the measurement was made? Explain.
Does the uncertainty principle set a limit to how well you can make any single measurement of position?
If you knew the position of an object precisely, with no uncertainty, how well would you know its momentum?
When you check the pressure in a tire, doesn’t some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertainty principle?
It has been said that the ground-state energy in the hydrogen atom can be precisely know but the excited states have some uncertainty in their values (an “energy width”). Is this consistent with the uncertainty principle in its energy from? Explain.
Which model of the hydrogen atom, the Bohr model or the quantum-mechanical mode, predicts that the electron spends more time near the nucleus?
The size of atoms varies by only a factor of three or so, from largest to smallest, yet the number of electrons varies form one to over 100. Explain.
Excited hydrogen and excited helium atoms both radiate light as they jump down to the n = 1, l = 0, mt = 0 state. Yet the two elements have very different emission spectra. Why?
How would the periodic table look if there were no electron spin but otherwise quantum mechanics were valid? Consider the first 20 elements or so.
Which of the following electron configurations are not allowed?(a) 1s22s22p43s24p2;(b) 1s22s22p8p3s1;(c) 1s22s22p63523p54s24d54f1? If not allowed, explain why.
In what column of the periodic table would you expect to find the atom with each of the following configuration?(a) 1s22s22p63s2;(b) 1s22s22p63s23p6;(c) 1s22s22p63s23p64s1;(d) 1s22s22p5;
Why do chlorine and iodine exhibit similar properties?
Explain why potassium and sodium exhibit similar properties.
The ionization energy for neon (Z = 10) is 21.6eV, and that for sodium (Z = 11) is 5.1eV. Explain the large difference.
Why does the cutoff wavelength in Fig. 28-11 imply a photon nature for light?
Why do we not expect perfect agreement between measured values of X-ray line wavelengths and those calculated using Bohr Theory as in Example 28-6?
How would you figure out which lines in an X-ray spectrum correspond to Ka, Kβ, L etc. transition?
Why do we expect electron transition deep within an atom to produce shorter wavelengths than transitions by outer electrons?
Compare spontaneous emission to stimulated emission.
How does laser light differ from ordinary light? How is it the same?
Explain how a 0.0005-W laser beam, photographed at a distance can seem much stronger than a 1000-W street lamp at the same distance.
Does the intensity of light from a laser fall off as the inverse square of the distance? Explain.
The neutrons in a parallel beam, each having kinetic energy 1/40eV, are directed through two slits 0.56mm apart. How far apart will the interference peaks be on a screen 1.0m away?
Bullets of mass 3.0g are fired in parallel paths with speeds of 220m/s through a hole 3.0mm in diameter, how far from the hole must you be to detect a 1.0-cm-diameter spread in the beam of bullets?
A proton is traveling with a speed of (6.560 ±0.012) x 105m/s. With what maximum accuracy can its position be ascertained?
If an electron’s position can be measured to an accuracy of 2.0 x 10–8 m, how accurately can its speed be known?
An electron remains in an excited state of an atom for typically 10–8s. What is the minimum uncertainty in the energy of the state (in eV)?
The Z0 boson, discovered in 1985, is the mediator of the weal nuclear force, and it typically decays very quickly. Its average rest energy is 91.19GeV, but its short lifetime shows up as an intrinsic width of 2.5GeV (rest energy uncertainty). What is the lifetime of this particle?
What is the uncertainty in the mass of a muon (m – 10.5.7MeV/c2), specified in eV/c2, given its lifetime of 2.20μs?
A free neutron (m = 1.67 x 10 – 27kg) has a mean life of 900s. What is the uncertainty in its mass (in kg)?
An electron and a 140-g baseball are each traveling 150m/s measured to an accuracy of 0.55%. Calculate and compare the uncertainty in position of each.
Estimate the lowest possible energy of a neutron contained in a typical nucleus of radius 1.0 X 10–15m.
Use the uncertainty principle to show that if an electron were present in the nucleus (r ≈ 10 – 15m), its kinetic energy (use relativity) would be hundreds of MeV. (Since such electron energies are not observed, we conclude that electrons are not present in the nucleus).
How accurately can the position of a 3.00-keV electron be measured assuming its energy is known to 1.00%?
For n = 6, what values can l have?
For n = 5, l = 3, what are the possible values of m1 and ms?
How many different states are possible for an electron whose principle quantum number is n = 4? Write down the quantum numbers for each state?
List the quantum numbers for each electron in the ground state of (a) Carbon (Z = 6),(b) Magnesium (Z = 12).
List the quantum numbers for each electron in the ground state of nitrogen (Z = 7).
Suppose a certain hydrogen atom has l = 4. What are the possible values for n, m1, and ms?
Calculate the magnitude of the angular momentum of an electron in the n = 4, l = 3 state of hydrogen.
If a hydrogen atom has m1 = – 3, what are the possible values of n, l, and ms?
Show that there can be 18 electrons in a “g” sub shell.
What is the full electron configuration in the ground state for elements with Z equal to? (a) 27,(b) 36,(c) 38?
What is the full electron configuration for? (a) Selenium (Se),(b) Gold (Au),(c) Radium (Ra)?
A hydrogen atom is in the 6s state. Determine(a) The principal quantum number,(b) The energy of the state,(c) The orbital angular momentum and its quantum number l, and(d) The possible values for the magnetic quantum number.
Estimate the binding energy of the third electron in lithium using the Bohr Theory.
Show that the total angular momentum is zero for a filled sub shell.
For each of the following atomic transitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is being violated; (a) 4p → 3p; (b) 2p → 1s; (c) 3d → 2d; (d) 4d → 3s; (e) 4s → 2p.
An excited H atom is in a 6d state.(a) Name all the state (n, l) to which the atom is “allowed” to jump with the emission of a photon.(b) How many different wave-lengths are there (ignoring fine (structure)?
What are the shortest-wavelength X-rays emitted by electrons striking the face of a 33.5-kV TV picture tube? What are the longest wavelengths?
If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tube have λ = 0.030nm, what is the voltage across the tube?
Show that the cutoff wavelength λ0 is given by where V is the X-ray tube voltage in volts.
Use the result of Example 28-6 to estimate the X-ray wavelength emitted when a Co (Z = 27) atom jumps from n = 2 to n = 1.
Estimate the wavelength for an n = 2 to n = 1 transition in iron (Z = 26).
Use the Bohr Theory to estimate the wavelength for an n = 3 to n = 1 transition in molybdenum (Z = 42). The measured value is 0.063nm. Why do we not expect perfect agreement?
A mixture of iron and an unknown material is bombarded with electrons. The wavelength of the Ka lines are 194pm for iron and 229 pm for the unknown. What is the unknown material?
A laser used to weld detached retinas puts out 28-ms-long pulses of 640-nm light which average 0.68-W output during a pulse. How much energy can be deposited per pulse and how many photons does each pulse contain?
A low-power laser used in a physics lab might have a power of 0.50mW and a beam diameter of 3.0mm. Calculate (a) The average light intensity of the laser beam, and (b) Compare it to the intensity of a lightbulb producing 40-W light viewed from 2.0m.
Estimate the angular spread of a laser beam due to diffraction if the beam emerges through a 3.0-mm-diameter mirror. Assume that λ = 694nm. What would be the diameter of this beam if it struck? (a) A satellite 300 km above the Earth, or (b) The Moon?
What is the wavelength of the He-Ne laser?
Use the uncertainty principle to estimate the position uncertainty for the electron in the ground state of the hydrogen atom.
An electron in the n = 2 state of hydrogen remains there on average about 10 – 8s before jumping to the n = 1 state. (a) Estimate the uncertainty in the energy of the n = 3 state.(b) What fraction of the transition energy is this?(c) What is the wavelength, and width (in nm), of this line in the
What are the largest and smallest possible values for the angular momentum L of an electron in the n = 5 shell?
Estimate (a) The quantum number l for the orbital angular momentum of the Earth about the Sun, and (b) The number of possible orientations for the plane of Earth’s orbit.
A 12-g bullet leaves a rifle at a speed of 180m/s. (a) What is the wavelength of this bullet?(b) If the position of the bullet is known to an accuracy of 0.60cm (radius of the barrel), what is the minimum uncertainty in its momentum?
Using the Bohr formula for the radius of an electron orbit, estimate the average distance from the nucleus for an electron in the innermost (n = 1) orbit of a uranium atom (Z = 92). Approximately how much energy would be required to remove this innermost electron?
An X-ray tube operates at 95kV with a current of 25mA and nearly all the electron energy goes into heat. If the specific heat of the 0.085-kg plate is 0.11 kcal/kg ∙ Co, what will be the temperature rise per minute if no cooling water is used?
The ionization (binding) energy of the outermost electron is boron is 8.2eV.(a) Use the Bohr model to estimate the “effective charge” Z eff, see by this electron. (b) Estimate the average orbital radius.
Use the Bohr Theory (especially Eq. 27-16) to show that the Moseley plot (Fig. 28-12) can be writtenWhere b ≈ 1, and evaluate a.
(a) Show that the number of different states for a given value of l is equal to 2(2l + 1). (b) What is this number for l = 0, 1, 2, 3, 4, 5, and 6?
Show that the number of different electron states possible for a given value of n is 2n2.
A beam of electrons with kinetic energy 45keV is shot through two narrow slits in a barrier. The slits are a distance 2.0 X 10–6m apart. If a screen is placed 35.0cm behind the barrier, calculate the spacing between the “bright” fringes of the interference pattern produced on the screen.
The angular momentum in the hydrogen atom is given both by the Bohr model and by quantum mechanics. Compare the results for n = 2.
An 1100-kg car is traveling with a speed of (22 ± 0.22) m/s. With what maximum accuracy can its position be determined?
An atomic spectrum contains a line with a wavelength centered at 488nm. Careful measurements show the line is really spread out between 487and 489 nm. Estimate the lifetime of the excited state that produced this line.
Protons are accelerated from rest across 550V. They are then directed at two slits 0.70mm apart. How far apart will the interference peaks be on a screen 28m away?
An electron and a proton, each initially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.
If the principal quantum number n were limited to the range from 1 to 6, how many elements would we find in nature?
If your de Broglie wavelength were 0.50m, how fast would you be moving if your mass is 75.0kg? Would you notice diffraction effects as you walk through a doorway? Approximately how long would it take you to walk through the doorway?
Suppose that the spectrum of an unknown element shows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown element is an ion with Z protons and one electron, determine Z and the element in question.
Photons of wavelength 0.154nm are emitted from the surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corresponds to the Ka line, what is the element?
Show that the diffractive spread of a laser beam ≈ λ/D as described in Section 28-11 is precisely what you might expect from the uncertainty principle.
What type of bond would you expect for? (a) The N2 molecule,(b) The HCI molecule(c) Fe atoms in a solid?
Describe how the molecule CaCl2 could be formed.
Does the H2 molecule have a permanent dipole moment? Does O2? Does H2O? Explain.
Although the molecule H3 is not stable, the ion H3+ is. Explain, using the Pauli Exclusion Principle.
The energy of a molecule can be divided into four categories.

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Fundamentals Of Hydraulic Engineering Systems 4th Edition Robert J. Houghtalen, A. Osman H. Akan, Ned H. C. Hwang - Solutions

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