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physics
modern physics

Questions and Answers of Modern Physics

(a) Show that for large n, the fractional difference in energy between state n and state n + 1 for a particle in a box is given approximately by (b) What is the approximate percentage energy
In 1985, a light pulse of 1.8 x 1012 photons was produced in an AT&T laboratory during a time interval of 8 x 10-15 s. The wavelength of the produced light was l = 2400 nm. Suppose all of the
This problem is one of estimating the time lag (expected classically but not observed) in the photoelectric effect, let the intensity of the incident radiation be 0.01 W/m2.(a) If the area of the
(Multiple choice)(1) The quantized character of electromagnetic radiation is revealed by (a) The Young double-slit experiment. (b) Diffraction of light by a small aperture. (c)
The Andromeda Nebula, at a distance of 2 x 1022 m from the Earth, radiates 8 x 1027 W in the spectral line of frequency 1420 MHz. Estimate the number of photons received per second when the nebula is
What is the force experienced by a mirror when it reflects all the light from a laser with a power of 10mW?
A crystalline specimen is irradiated with X-rays of wavelength A. Bragg reflexion is observed at 23.0◦, Φ and 73.5◦ (23.0◦ < Φ < 73.5◦), with respect to the direction of the incident beam.
In an experiment on the photoelectric effect it is observed that for light of wavelength 500 nm, a slopping potential of 0.2.5V is required to cut off the current of photoelectrons, whereas at a
What is the velocity of an electron which has a kinetic energy equal to the energy of a photon of wavelength 1nm?
To study crystal diffraction we need wavelengths of about 0.5 x 10–10 m. what would be the corresponding kinetic energies in eV of (a) A photon,(b) An electron, and(c) A neutron?
Estimate the speed and the de Broglie wavelength of an oxygen molecule at room temperature.
Use the de Brogue relation between the wavelength and the linear momentum of a non-relativistic particle, and the Planck relation between frequency and quantum energy, to obtain the phase and group
Free neutrons have decay constant of 1.10 x 10-3 s-1. If the de Broglie wavelength of the neutrons in a parallel beam is 1 nm, determine the distance from the source where the beam intensity has
Using Bohr theory derive and expression for the frequencies at which light is absorbed by hydrogen atoms in their ground state. Why would these frequencies be slightly different for tritium atoms?
Positronium is a hydrogen-like system with the proton replaced by a positron. Use the Bohr model to calculate the energy of the system in its ground state.
Calculate the velocity of an electron in the third Bohr orbit (n = 3) of the hydrogen atom.
An atom has energy levels En = – A/n2 where n is an integer and A is a constant. Among the spectral lines that the atom can absorb at room temperature are two adjacent lines with wavelengths 97.5nm
A spectrometer of resolving power 5 x 105 is used to observe the Balmer series in the hydrogen spectrum (transitions for which the principal quantum number changes from n > 2 to n = 2. Find the
State the Schr?dinger equation for a particle of mass m moving in the xy-plane subject to a potential energy V(x, y). What is the probability of finding it in a small area ?S centred at the point (x,
Calculate the possible values of the energy of a particle of mass m situated inside a deep one-dimensional potential well of width a described by V = 0 for 0 ≤ x ≤ a and V = ∞ elsewhere. An
Consider particles of mass m and energy E moving along the x-axis under the influence of a potential V(x). The particles have energy E > 0 and the potential had the from V(x) = 0 for x < 0, V(x) = V0
238U decays with a half-life of 4.51 x 109 years, the decay series eventually ending at 206Pb, which is stable. A rock sample analysis shows that the ratio of the numbers of atoms of 206Pb to 238U is
It is proposed to use 113Cd48 as an attenuator in a nuclear pile. Calculate the thickness required to attenuate a neutron beam to 0.01% of its original intensity it if has a density of 8.7 x 103 kg
What type of bonding mechanism would you expect for(a) HF,(b) KBr,(c) N2?
What kind of bonding mechanism would you expect for(a) The N2 molecule,(b) The KF molecule,(c) Ag atoms in a solid?
Calculate the separation of Na+ and Cl– ions for which the potential energy is -1.52 eV.
The dissociation energy of Cl2 is 2.48 eV. Consider the formation of an NaCl molecule according to the reactionNa + ½Cl2 → NaClDoes this reaction absorb energy or release energy? How much energy
The dissociation energy is sometimes expressed in kilocalories per mole (kcal/mol).(a) Find the relation between the units eV/molecule and kcal/mol.(b) Find the dissociation energy of molecular NaCl
The equilibrium separation of the HF molecule is 0.0917 nm and its measured electric dipole moment is 6.40 × 10-30 C · m. What percentage of the bonding is ionic?
Do Problem 9 for CsCl, for which the equilibrium separation is 0.291 nm and the measured electric dipole moment is 3.48 × 10-29 C · m.
The dissociation energy of LiCl is 4.86 nm and the equilibrium separation is 0.202 nm. The electron affinity of chlorine is 3.62 eV, and the ionization energy of lithium is 5.39 eV. Determine the
The equilibrium separation of the K+ and Cl- ions in KCl is about 0.267 nm. (a) Calculate the potential energy of attraction of the ions assuming them to be point charges at this separation. (b) The
Indicate the mean value of r for two vibration levels in the potential-energy curve for a diatomic molecule and show that because of the asymmetry in the curve, rav increases with increasing
Calculate the potential energy of attraction between the Na+ and Cl? ions at the equilibrium separation r0 = 0.236 nm and compare this result with the dissociation energy given in Figure. What is the
The equilibrium separation of the K+ and F– ions in KF is about 0.217 nm.(a) Calculate the potential energy of attraction of the ions, assuming them to be point charges at this separation.(b) The
Assume that the core repulsion can be represented by a potential energy of the form Urep = C/rn. So the total potential energy is Use the fact that dU/dr = 0 at r = r0, and the results for Urep at r
(a) Find Urep at r = r0 for NaCl.(b) Assume Urep = C/rn and find C and n for NaCl.
Find other elements with the same subshell electron configuration in the two outermost orbitals as carbon. Would you expect the same type of hybridization for these elements as for carbon?
The characteristic rotational energy E0r for the rotation of the N2 molecule is 2.48 × 10-4 eV. From this find the separation distance of the N atoms in N2.
The separation of the O atoms in O2 is actually slightly greater than the 0.1 nm used in Example 38-3, and the characteristic energy of rotation E0r is 1.78 × 10-4 eV rather than the result obtained
Show that the reduced mass is smaller than either mass in a diatomic molecule, and calculate it for(a) H2,(b) N2,(c) CO, and(d) HCl. Express your answers in unified mass units.
The equilibrium separation between the nuclei of the LiH molecule is 0.16 nm. Determine the energy separation between the ℓ = 3 and ℓ = 2 rotational levels of this diatomic molecule.
Repeat Problem 24 for LiD, where D is the symbol for deuterium. Note that replacing the proton by the deuteron does not change the equilibrium separation between the nuclei of the molecule.
Derive Equations 38-14 and 38-15 for the moment of inertia in terms of the reduced mass of a diatomicmolecule.
Use the separation of the K+ and Cl– ions given in Problem 12 and the reduced mass of KCl to calculate the characteristic rotational energy E0r.
The central frequency for the absorption band of HCl shown in Figure is at f?= 8.66 ? 1013 Hz, and the absorption peaks are separated by about ?f?= 6 ? 1011 Hz. Use this information, to find (a) The
Calculate the effective force constant for HCl from its reduced mass and the fundamental vibrational frequency obtained fromFigure.
Two objects of mass m1 and m2 are attached to a spring of force constant K and equilibrium length r0 . (a) Show that when m1 is moved a distance ?r1 from the center of mass, the force exerted by the
Calculate the reduced mass for the H35Cl and H37Cl molecules and the fractional difference ??μ/μ. Show that the mixture of isotopes in HCl leads to a fractional difference in the frequency of a
In calculating the rotational energy levels of a diatomic molecule, we did not consider rotation of the molecule about the line joining the atoms.(a) Estimate the moment of inertia of the H2 molecule
Suppose that hard spheres of radius R are located at the corners of a unit cell with a simple cubic structure.(a) If the hard spheres touch so as to take up the minimum volume possible, what is the
Calculate the distance r0 between the K+ and the Cl– ions in KCl, assuming that each ion occupies a cubic volume of side r0. The molar mass of KCl is 74.55 g/mol and its density is 1.984 g/cm3.
The distance between the Li+ and Cl– ions in LiCl is 0.257 nm. Use this and the molecular mass of LiCl (42.4 g/mol) to compute the density of LiCl.
Find the value of n?in Equation 38-32 that gives the measured dissociation energy of 741 kJ/mol for LiCl, which has the same structure as NaCl and for which r0 = 0.257 nm.
Suppose identical bowling balls of radius R are packed into a hexagonal close-packed structure. What fraction of the available volume of the unit cell is filled by the bowling balls?
The donor energy levels in an n-type semiconductor are 0.01 eV below the conduction band. Find the temperature for which kT = 0.01 eV.
The relative binding of the extra electron in the arsenic atom that replaces an atom in silicon or germanium can be understood from a calculation of the first Bohr orbit of this electron in these
The ground-state energy of the hydrogen atom is given by Modify this equation in the spirit of Problem 43 by replacing ?0 by ??0 and me by an effective mass for the electron to estimate the binding
A doped n-type silicon sample with 1016 electrons per cubic centimeter in the conduction band has a resistivity of 5 × 10-3 Ω · m at 300 K. Find the mean free path of the electrons. Use the
Simple theory for the current versus the bias voltage across a pn junction yields the equationI = I0( eeVb/kT – 1)Sketch I versus Vb for both positive and negative values of Vb using this
For a temperature of 300 K, use the equation in Problem 49 to find the bias voltage Vb for which the exponential term has the value(a) 10 and(b) 0.1.
Germanium can be used to measure the energy of incident particles. Consider a 660-keV gamma ray emitted from 137Cs.(a) Given that the band gap in germanium is 0.72 eV, how many electron–hole pairs
Make a sketch showing the valence and conduction band edges and Fermi energy of a pn-junction diode when biased(a) In the forward direction and(b) In the reverse direction.
A "good" silicon diode has the current–voltage characteristic given in Problem 49. Let kT = 0.025 eV (room temperature) and the saturation current I0 = 1 nA.(a) Show that for small
A slab of silicon of thickness t = 1.0 mm and width ω = 1.0 cm is placed in a magnetic field B = 0.4 T. The slab is in the xy plane, the magnetic field points in the positive z direction. When a
Why would you expect the separation distance between the two protons to be larger in the H2+ ion than in the H2 molecule?
What kind of bonding mechanism would you expect for(a) The HCl molecule(b) The O2 molecule,(c) Cu atoms in a solid?
Why does an atom usually absorb radiation only from the ground state whereas a diatomic molecule can absorb radiation from many different rotational states?
The equilibrium separation of CsF is 0.2345 nm. If its bonding is 70% ionic, what is its electric dipole moment.
Show that when one atom in a diatomic molecule is much more massive than the other the reduced mass is approximately equal to the mass of the lighter atom.
The equilibrium separation between the nuclei of the CO molecule is 0.113 nm. Determine the energy difference between the ℓ = 2 and ℓ = 1 rotational energy levels of this molecule.
The effective force constant for the HF molecule is 970 N/m. Find the frequency of vibration for this molecule.
The frequency of vibration of the NO molecule is 5.63 × 1013 Hz. Find the effective force constant for NO.
The force constant of the hydrogen bond in the H2 molecule is 580 N/m. Obtain the energies of the four lowest vibrational levels of H2, HD, and D2 molecules, and the wavelengths of photons resulting
The potential energy between two atoms in a molecule can often be described rather well by the Lenard-Jones potential, which can be writtenWhere U0 and a are constants. Find the interatomic
In this problem you are to find how the van der Waals force between a polar and a nonpolar molecule depends on the distance between the molecules. Let the dipole moment of the polar molecule be in
Find the dependence of the force on separation distance between two polar molecules.
Use the infrared absorption spectrum of HCl in Figure to obtain (a) The characteristic rotational energy E0r (in eV) (b) The vibrational frequency f and the vibrational energy hf (in eV).
For a molecule such as CO, which has a permanent electric dipole moment, radiative transitions obeying the selection rule Δℓ = ±1 between two rotational energy levels of the same vibrational
Use the results of Problem 16 to calculate the vibrational frequency of the LiCl molecule. To do this, expand the potential about r = r0 where r0 is the equilibrium separation, in a Taylor series.
Repeat Problem 74 for the NaCl molecule.
A one-dimensional model of an ionic crystal consists of a line of alternating positive and negative ions with distance r0 between each ion.(a) Show that the potential energy of attraction of one ion
(Multiple choice)(1)Which of the following elements are most likely to serve as acceptor impurities in germanium?(a) Bromine,(b) Gallium,(c) Silicon,(d) Phosphorus,(e) Magnesium.(2)Which of the
1. Would you expect the NaCl molecule to be polar or nonpolar?2. Would you expect the N2 molecule to be polar or nonpolar?3. Does neon occur naturally as Ne or Ne2? Why?
1. How does the effective force constant calculated for the CO molecule in Example 38-4 compare with the force constant of an ordinary spring? 2. In Figure for the pnp-transistor amplifier, suppose
1. What type of semiconductor is obtained if silicon is doped with(a) Aluminum and(b) Phosphorus?2. What type of semiconductor is obtained if silicon is doped with(a) Indium and(b) Antimony?
1. Show that when an intrinsic semiconductor carries a current in a transverse magnetic field no Hall voltage is developed across the sample.2. Explain why the moment of inertia of a diatomic
1. The semiconducting compound CdSe is widely used for light emitting diodes (LEDs). The energy gap in CdSe is 1.8 eV. What is the frequency of the light emitted by a CdSe LED?2. The resistivity of a
In this problem, you will calculate the difference in the time of arrival of two neutrinos of different energy from a supernova that is 170,000 light-years away. Let the energies of the neutrinos be
(Multiple choice)(1) True or false:(a) All baryons are hadrons.(b) All hadrons are baryons.(2) True or false:Mesons are spin-1/2 particles.(3) True or false:(a) Leptons consist of three quarks.(b)
How are baryons and mesons similar? How are they different?
The muon and the pion have nearly the same mass. How do these particles differ?
How can you tell whether a decay proceeds via the strong interaction or the weak interaction?
Two pions at rest annihilate according to the reaction π+ + π– → γ + γ.(a) Why must the energies of the two g rays be equal?(b) Find the energy of each γ ray.(c) Find the wavelength of each
Find the minimum energy of the photon needed for the following pair-production reactions:(a) γ → π+ + π – ,(b) γ → π+ π – , and(c) γ → m– + m+ .
State which of the decays or reactions that follow violate one or more of the conservation laws, and give the law or laws violated in each case:(a) p + → n + e + + ve,(b) n → p + +
Determine the change in strangeness in each reaction that follows, and state whether the reaction can proceed via the strong interaction, the weak interaction, or not at all:(a) Ω– → Ξ0 +
Determine the change in strangeness for each decay, and state whether the decay can proceed via the strong interaction, the weak interaction, or not at all:(a) Ω– → Λ0 + K– and(b) (0 → p
(a) Which of the following decays of the t particle is possible?τ → μ– + vμ + vττ → μ– + vμ + vτ(b) Explain why the other is not possible.(c) Calculate the kinetic
Consider the following decay chain:Ω– → Ξ0 + π –Ξ0 → ∑+ + e – + veπ – → μ – + vμ∑+ → n + π+π+ → μ + + vμμ + → e + + v μ

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