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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

For the three vectors shown in FIGURE EX3.20, A̅ + B̅ + C̅ = 1ĵ.What is vector B̅?a. Write B̅ in component form.b. Write B̅ as a magnitude and a direction.FIGURE EX3.20:
LetA̅ = 4î - 2ĵ, B̅ = -3î + 5ĵ, and F̅ = A̅ - 4B̅.a. Write vector F̅ in component form.b. Draw a coordinate system and on it show vectors A̅, B̅, and F̅.c. What are the magnitude and
Let A̅ = 4î - 2ĵ, B̅ = -3î + 5ĵ, and E̅ = 2 A̅ + 3B̅.a. Write vector E̅ in component form.b. Draw a coordinate system and on it show vectors A̅ , B̅, and Eu.c. What are the magnitude
Let A̅ = 4î - 2ĵ, B̅ = -3î + 5̂ĵ, and C̅ = A̅ + B̅.a. Write vector C̅ in component form.b. Draw a coordinate system and on it show vectors A̅ , B̅, and C̅.c. What are the magnitude
Let A̅ = 2î + 3ĵ, B̅ = 2î - 4ĵ, and C̅ = A̅ + B̅.a. Write vector C̅ in component form.b. Draw a coordinate system and on it show vectors A̅, B̅ and C̅.c. What are the magnitude and
Draw each of the following vectors, label an angle that specifies the vector’s direction, and then find the vector’s magnitude and direction.a. A̅ = 3.0î + 7.0ĵb. a̅ = (-2.0î +
Draw each of the following vectors. Then find its x- and y-components.a. v̅ = (7.5 m/s, 30° clockwise from the positive y-axis)b. a̅ = (1.5 m/s2, 30° above the negative x-axis)c. F̅ = (50.0 N,
Draw each of the following vectors. Then find its x- and y-components.a. a̅ = (3.5 m/s2, negative x-direction)b. v̅ = (440 m/s, 30° below the positive x-axis)c. r̅ = (12 m, 40° above the
a. What are the x- and y-components of vector E̅ shown in FIGURE EX3.3 in terms of the angle θ and the magnitude E̅?b. For the same vector, what are the x- and y-components in terms of the angle
You are given the kinematic equation or equations that are used to solve a problem. For each of these, you are to:
You are given the kinematic equation or equations that are used to solve a problem. For each of these, you are to:
You are given the kinematic equation or equations that are used to solve a problem. For each of these, you are to:
You are given the kinematic equation or equations that are used to solve a problem. For each of these, you are to:
FIGURE EX2.4 is the position-versus-time graph of a jogger. What is the jogger’s velocity at t = 10 s, at t = 25 s, and at t = 35 s?FIGURE EX2.4:
For Questions 1 through 3, interpret the position graph given in each figure by writing a very short “story” of what is happening. Be creative! Have characters and situations! Simply saying that
For Questions 1 through 3, interpret the position graph given in each figure by writing a very short “story” of what is happening. Be creative! Have characters and situations! Simply saying that
For Questions 1 through 3, interpret the position graph given in each figure by writing a very short “story” of what is happening. Be creative! Have characters and situations! Simply saying that
Write a short description of a real object for which Figure P1.60 would be a realistic position-versus-time graph.FIGURE P1.60:
a. Complete the motion diagram by adding acceleration vectors.b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don’t forget to include enough information to
a. Complete the motion diagram by adding acceleration vectors.b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don’t forget to include enough information to
a. Complete the motion diagram by adding acceleration vectors.b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don’t forget to include enough information to
a. Complete the motion diagram by adding acceleration vectors.b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Don’t forget to include enough information to
Show a motion diagram. For each of these problems, write a one or two sentence “story” about a real object that has this motion diagram. Your stories should talk about people or objects by name
A two-element bar as shown in Figure PA-12 with element lengths L, cross-sectional area A, and Young?s modulus E can be shown to have a stiffness matrix of ? Show that the det (|k|) = 0 and hence
Determine [C]-1
A large plate of stainless steel with thickness of 5 cm and thermal conductivity of k = 15W/ m-oC is subjected to an internal uniform heat generation throughout the plate at constant rate of Q = 10 ?
An aircraft cabin window of circular cross section and simple supports all around as shown in the following is made of polycarbonate with E = 0:345 ? 106 psi, n = 0:36, radius = 20 in., and thickness
For the cylindrical vessel with hemispherical ends (heads) under uniform internal pressure of intensity p ? 500 psi shown in Figure P9?21, determine the maximum von Mises stress and where it is
Write a computer program to solve plane stress problems using the LST element.
Use the LST element to solve Example 6.2. Compare the results. In example 6.2 For a thin plate subjected to the surface traction shown in Figure 6?16, determine the nodal displacements and the
How would you treat a linearly varying thickness for a three-noded triangle?
Compute the stiffness matrix of element 1 of the two-triangle element model of the rectangular plate in plane stress shown in the following figure. Then use it to compute the stiffness matrix of
Show that the normalization constant Anfor the wave functions of a particle in a rigid box has the value given in Equation 40.26. n= 1, 2, 3, ... A,= A,= VI
What is the probability that an electron will tunnel through a 0.45 nm gap from a metal to a STM probe if the work function is 4.0 eV?
Tennis balls traveling faster than 100 mph routinely bounce off tennis rackets. At some sufficiently high speed, however, the ball will break through the strings and keep going. The racket is a
a. What is the probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV?b. The probe passes over an atom that is 0.050 nm
In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. FIGURE CP40.47 is a one-dimensional
In a nuclear physics experiment, a proton is fired toward a Z = 13 nucleus with the diameter and neutron energy levels shown inFigure 40.17. The nucleus, which was initially in its ground state,
A proton’s energy is 1.0 MeV below the top of a 10-fm-wide energy barrier. What is the probability that the proton will tunnel through the barrier?
Even the smoothest mirror finishes are “rough” when viewed at a scale of 100 nm. When two very smooth metals are placed in contact with each other, the actual distance between the surfaces varies
Figure 40.17showed that a typical nuclear radius is 4.0 fm. As you€™ll learn in Chapter 42, a typical energy of a neutron bound inside the nuclear potential well is En= -20 MeV. To find out
A particle of mass m has the wave function when it is in an allowed energy level with E = 0.a. Draw a graph of ψ(x) versus x.b. At what value or values of x is the particle most likely to be
a. Derive an expression for the classical probability density Pclass(y) for a ball that bounces between the ground and height h. The collisions with the ground are perfectly elastic.b. Graph your
a. Derive an expression for the classical probability density Pclass(x) for a simple harmonic oscillator with amplitude A.b. Graph your expression between x = -A and x = +A.c. Interpret your graph.
a. Determine the normalization constant A1 for the n = 1 ground-state wave function of the quantum harmonic oscillator. Your answer will be in terms of b.b. Write an expression for the probability
Show that the constant b used in the quantum-harmonic oscillator wave functions(a) Has units of length(b) Is the classical turning point of an oscillator in the n = 1 ground state.
A typical electron in a piece of metallic sodium has energy -E0 compared to a free electron, where E0 is the 2.7 eV work function of sodium.a. At what distance beyond the surface of the metal is the
For a particle in a finite potential well of width L and depth U0, what is the ratio of the probability Prob(in δx at x = L + η) to the probability Prob(in δx at x = L)?
For the quantum-well laser ofFigure 40.16, estimate the probability that an electron will be found within one of the GaAlAs layers rather than in the GaAs layer. Explain your reasoning. GAAIAS GạAs
A neutron is confined in a 10-fm-diameter nucleus. If the nucleus is modeled as a one-dimensional rigid box, what is the probability that a neutron in the ground state is less than 2.0 fm from the
Consider a particle in a rigid box of length L. For each of the states n = 1, n = 2, and n = 3:a. Sketch graphs of |ψ(x)|2. Label the points x = 0 and x = L.b. Where, in terms of L, are the
A particle confined in a rigid one-dimensional box of length 10 fm has an energy level En = 32.9 MeV and an adjacent energy level En+1 = 51.4 MeV.a. Determine the values of n and n + 1.b. Draw an
a. Derive an expression for λ2→1, the wavelength of light emitted by a particle in a rigid box during a quantum jump from n = 2 to n = 1.b. In what length rigid box will an electron undergoing a 2
Model an atom as an electron in a rigid box of length 0.100 nm, roughly twice the Bohr radius.a. What are the four lowest energy levels of the electron?b. Calculate all the wavelengths that would be
A 2.0-μm-diameter water droplet is moving with a speed of 1.0 mm/s in a 20@mm@long box.a. Estimate the particle’s quantum number.b. Use the correspondence principle to determine whether quantum
Suppose that ψ1(x) and ψ2(x) are both solutions to the Schrödinger equation for the same potential energy U(x). Prove that the superposition ψ(x) = Aψ1(x) + Bψ2(x) is also a solution to the
An electron approaches a 1.0-nm-wide potential-energy barrier of height 5.0 eV. What energy electron has a tunneling probability of(a) 10%,(b) 1.0%,(c) 0.10%?
Verify that the n = 1 wave function ψ1(x) of the quantum harmonic oscillator really is a solution of the Schrödinger equation. That is, show that the right and left sides of the Schrödinger
Use the data fromFigure 40.24 to calculate the first three vibrational energy levels of a C = O carbon-oxygen double bond. Transmission (%) 100- 75- 1-2 transition of a C-CH, bond 50- 1-2
An electron is confined in a harmonic potential well that has a spring constant of 12.0 N/m. What is the longest wavelength of light that the electron can absorb?
An electron in a harmonic potential well absorbs a photon with a wavelength of 400 nm as it undergoes a 1 → 2 quantum jump. What wavelength is absorbed in a 1 → 3 quantum jump?
An electron confined in a harmonic potential well emits a 1200 nm photon as it undergoes a 3 → 2 quantum jump. What is the spring constant of the potential well?
Two adjacent energy levels of an electron in a harmonic potential well are known to be 2.0 eV and 2.8 eV. What is the spring constant of the potential well?
An electron is confined in a harmonic potential well that has a spring constant of 2.0 N/m.a. What are the first three energy levels of the electron?b. What wavelength photon is emitted if the
The graph in FIGURE EX40.16 shows the potential-energy function U(x) of a particle. Solution of the Schrödinger equation finds that the n = 3 level has E3= 0.5 eV and that the n = 6 level has E6=
Sketch the n = 1 and n = 7 wave functions for the potential energy shown in FIGURE EX40.15. U(x) ↑ E, E FIGURE EX40.15
Sketch the n = 8 wave function for the potential energy shown in FIGURE EX40.14. U(x) Eg L FIGURE EX40.14 8
Sketch the n = 4 wave function for the potential energy shown in FIGURE EX40.13. U(x) E4 FIGURE EX40.13 8 8.
A helium atom is in a finite potential well. The atom’s energy is 1.0 eV below U0. What is the atom’s penetration distance into the classically forbidden region?
An electron in a finite potential well has a 1.0 nm penetration distance into the classically forbidden region. How far below U0 is the electron’s energy?
The energy of an electron in a 2.00-eV-deep potential well is 1.50 eV. At what distance into the classically forbidden region has the amplitude of the wave function decreased to 25% of its value at
An electron has a 0.0100 probability (a 1.00% chance) of tunneling through a potential barrier. If the width of the barrier is doubled, will the tunneling probability be 0.0050, 0.0025, or 0.0001?
A finite potential well has depth U0 = 2.00 eV. What is the penetration distance for an electron with energy(a) 0.50 eV,(b) 1.00 eV(c) 1.50 eV?
Four quantum particles, each with energy E, approach the potential-energy barriers seen in FIGURE Q40.8 from the left. Rank in order, from largest to smallest, the tunneling probabilities
a. Sketch graphs of the probability density |Ïˆ(x)|2 for the four states in the finite potential well of Figure 40.14a. Stack them vertically, similar to theFigure 40.14agraphs of
FIGURE Q40.7 shows two possible wave functions for an electron in a linear triatomic molecule. Which of these is a bonding orbital and which is an antibonding orbital? Explain how you can distinguish
Show that the penetration distance h has units of m.
Consider a quantum harmonic oscillator.a. What happens to the spacing between the nodes of the wave function as |x| increases? Why?b. What happens to the heights of the antinodes of the wave function
A 16-nm-long box has a thin partition that divides the box into a 4-nm-long section and a 12-nm-long section. An electron confined in the shorter section is in the n = 2 state. The partition is
Rank in order, from largest to smallest, the penetration distances ηato ηcof the wave functions corresponding to the three energy levels in FIGURE Q40.5. LELELE 16 eV -10 eV 10 eV 10 eV 5 eV 5 eV
FIGURE EX40.5 is the probability density for an electron in a rigid box. What is the electron??s energy, in eV? O nm 0.45 nm FIGURE EX40.5
What is the quantum number of the particle in FIGURE Q40.4? How can you tell? E FIGURE Q40.4
FIGURE EX40.4 shows the wave function of an electron in a rigid box. The electron energy is 12.0 eV. What is the energy, in eV, of the next higher state? (x) FIGURE EX40.4
A particle in a potential well is in the n = 5 quantum state. How many peaks are in the probability density P(x) = |ψ(x)|2?
FIGURE EX40.3 shows the wave function of an electron in a rigid box. The electron energy is 25 eV. How long is the box? (x) FIGURE EX40.3
The correspondence principle says that the average behavior of a quantum system should begin to look like the Newtonian solution in the limit that the quantum number becomes very large. What is meant
An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is 600 nm. How long is the box?
FIGURE Q40.1 shows the de Broglie waves of three equal- mass particles. Which one is moving most slowly? Explain. a b. FIGURE Q40.1
The electrons in a rigid box emit photons of wavelength 1484 nm during the 3 → 2 transition.a. What kind of photons are they—infrared, visible, or ultraviolet?b. How long is the box in which the
Consider the electron wave function where x is in nm.a. Determine the normalization constant c.b. Draw a graph of ψ(x) over the interval -5 nm ?? x ?? 5 nm. Provide numerical scales on both axes.c.
The wave function of a particle is and zero elsewhere.a. You will learn in Chapter 40 that the wave function must be a continuous function. Assuming that to be the case, what can you conclude about
The wave function of a particle is where b is a positive constant. Find the probability that the particle is located in the interval -b ?? x ?? b. b ¥(x)= ㅠ(x2 + b?) IT
The probability density of finding a particle somewhere along the x-axis is 0 for x < 1 mm. At x = 1 mm, the probability density is c. For x ≥ 1 mm, the probability density decreases by a factor
a. Starting with the expression Δf Δt ≈ 1 for a wave packet, find an expression for the product ΔE Δt for a photon.b. Interpret your expression. What does it tell you?c. The Bohr model of
A small speck of dust with mass 1.0 × 10-13g has fallen into the hole shown in FIGURE P39.46 and appears to be at rest. According to the uncertainty principle, could this particle have enough energy
Soot particles, from incomplete combustion in diesel engines, are typically 15 nm in diameter and have a density of 1200 kg/m3. FIGURE P39.45 shows soot particles released from rest, in vacuum, just
Physicists use laser beams to create an atom trap in which atoms are confined within a spherical region of space with a diameter of about 1 mm. The scientists have been able to cool the atoms in an
Heavy nuclei often undergo alpha decay in which they emit an alpha particle (i.e., a helium nucleus). Alpha particles are so tightly bound together that it’s reasonable to think of an alpha
You learned in Chapter 37 that, except for hydrogen, the mass of a nucleus with atomic number Z is larger than the mass of the Z protons. The additional mass was ultimately discovered to be due to
What is the smallest one-dimensional box in which you can confine an electron if you want to know for certain that the electron’s speed is no more than 10 m/s?

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