PHY 222 final
Electrons with energy of 25 eV have a wavelength of ~0.25 nm. If we send these electrons thru the same 2 slits (d=0.13 mm) we use to produce a visible light interference pattern what is the spacing (in mm) between the maxima on a screen 2.3 m away?
((2.3)(0.25e-9))/(0.13e-3)=4.423
An electron in a hydrogen atom makes a transition from the n=26 to the n=3 energy state. Determine the wavelength of the emitted photon (in nm).
(1.097e7((1/3^2)-(1.26^2))^-1=831
Electrons are ejected from a metal surface with energies ranging up to 5.0 eV when light with a wavelength of 585 nm is used. What is the work function of the metal in units of eV?
(1240/585)-0.5=1.62
A laser emits photons continuously at a rate of 4.8*10^16/s. If the wavelength of the photons is 445 nm, what is the laser power in mW?
(4.8e16)(6.62e-34)(3e8)/(445e-9)=21.4
What is the deBroglie wavelength (in nm) of a neutron (m=1.67x10^-27 kg) moving with a speed of 70 m/s?
(6.625e-34)/(1.67e-27*70)=5.67
A beam of light A has twice the wavelength but the same intensity as beam B. The number of photons that hit a given area in a given time, when illuminated by beam B is
1/2 the number that hit when the area is illuminated by beam A
The radius of an atomic nucleus is of the order of
10e-15
The half-life if 14C is 5730 years. Suppose an ancient bone is found in which the ratio of 14C/12C is 1/4 that found in the atmosphere and in living plants and animals. Approximately how old is the bone?
12000
A gamma ray photo has an energy of 1.52 GeV. (1 GeV = 10^9 eV). What is the wavelength of the gamma ray in fm?
1240/(1.52e9)=0.815
What is the wavelength (in nm) of a photon with energy E = 2.45 eV?
1240/2.45 = 506
A stream of electrons of energy E is incident on a potential barrier of the height U and thickness d. Even thougth U>E, 5% of the electrons tunnel through the barrier. If the thickness of the barrier decreases to 0.65 d, what percentage of the electrons will tunnel through?
14
A radioactive substance has a mean-life t of 16 years. Assume we start with 161 kg of the substance. How many kg of the substance will be left after 32 years?
161e(-32/16)=21.78
Assume that in an atom the subshell n=7, I=4 is completely filled. How many electrons does this subshell hold?
18 4(x)+2 4(4)+2=18
Which of the following condensed notations gives the lowest energy electronic configuration for doubly ionized Mg?
1s^2, 2s^2, 2p^6
The energy of a photon that has a wavelength of 9.0 m is _____J
2.23-26
228/90Th emits a gamma ray. What is the resulting nucleus?
228/90 Th
The isotope 234/92U undergoes 5 successive alpha decays. Identify the correct decay chain.
230/90Th --> 226/88Ra --> 222/86Rn --> 218/84Po --> 214/82Pb
Suppose a Uranium 238 nucleus "swallows" a neutron and then decays not by fission but by beta decay, emitting an electron and an anti-neutrino. Which nucleus remains after this decay?
239 Np
Blue light of wavelength λ passes thru a single slit of width a and forms a diffraction pattern on a screen. If the blue light is replaced by red light of wavelength 2λ, the original diffraction pattern is reproduced if the slit is changed to what?
2a
A hypothetical atom has 3 energy states. Assuming all transitions are possible, how many spectral lines can this atom produce?
3
How many of the following statements about the photoelectric effect are true?
3
Photons with λ= 250 nm (hf = 5 eV) hit a metal surface and emit photoelectrons with a maximum kinetic energy E=2.0 eV. What is the work function of the metal?
3 eV
Which of the following (n, l, m, m) combinations is impossible for an electron in a hydrogen atom?
3, 1, -2, 1/2
An excited hydrogen electron is in the principal shell n=3. Which of the following is a possible set of quantum numbers (n,l,m,ms) for the electron's state?
3, 2, -2, -1/2
A 1 ns laser pulse from a neodymium-YAG laser, at 532 nm, contains 5 J. What is the energy of photon in the pulse in units of eV? (1 eV=1.6*10^-19 J)
3.74e-19
Each proton-proton cycle generates 26.7 MeV of energy. If 3.8 Watts are generated via the proton-proton cycle, how many billion neutrinos are produced?
3.8/(26.7e6)(1.6e-19)=2.205
In 140 seconds, the number of radioactive nuclei decreases to 1/16 of the number present initially. What is the half-life (in s) of the material?
35 (140/4) = 35
An electron in a hydrogen atom makes a transition from the n=8 to the n=2 energy state. Determine the wavelength of the emitted photon (in nm)
389
A group of quantum state of the hydrogen atom has n=4. How many values of l are possible for the states in this group?
4
A partial energy level spectrum of hypothetical element X is given below. Of the transitions listed below, which one produces the shortest wavelength photon?
4 to 1
If the orbital angular momentum is I=4, what is the magnitude of the orbital angular momentum, and what is the largest value its projection can have along any axis in units of h?
4.47; 4
A hydrogenic He ion is excited from its ground state to the state with n=2. How much energy (in eV) must be absorbed by the ion?
40.8
A hydrogenic ion with Z=6 is excited from its ground state with n=8. How much energy (in eV) must be absorbed by the ion?
482
The figure below shows different ways to connect a light bulb to a battery with wires. Which of the bulbs will light up?
5
An ideal polarizer will transmit 50% of unpolarized light incident on it. How much light is transmitted by 2 ideal polarizers in series that are oriented with their transmission axes parallel to each other?
50%
Light incidient on a 0.15 mm wide slit forms a diffraction pattern on a screen 6 m away. If the first minimum of the diffraction pattern is 2 cm from the central peak, what is the wavelength of the incident light?
500 nm
At what rate must Uranium 235 undergo fission by neutron bombardment to generate energy at a rate of 534 W (1W=1J/s)? Assume each fission releases 200 MeV of energy.
534/(200)(1.6023e-13)=1.666
A hydrogen atom is in a state for which the principle quantum number is n=3. How many possible such states are there for which the quantum number is m=0?
6
A group of quantum states of the hydrogen atom has n=5. A subgroup of this group has l=3. How many values of m are possible for the states in this subgroup?
7
A hydrogen atom electron is excited to an energy of -13.6/4 eV. How many different quantum states are there with this energy?
8
If the orbital angular momentum is 4, how many different projections along the z-axis are possible?
9
What are the changes in the mass number A and the atomic number Z of a nucleus that undergoes beta decay?
A is unchanged, Z decreases by 1
Assume that in the experiment shown below electrons are ejected with some kinetic energy when green light hits a metal surface. Which of the statements below is incorrect?
A less intense green beam will eject electrons of less kinetic energy.
Which statement below is true?
Consider the photoelectric effect. The greater the work function of the target, the greater is the cutoff frequency.
What is the significance of the quantum number m when specifying energy eigenfunction or orbital of atoms?
It indicates the orientation of the orbital
What is the definition of the nuclear binding energy?
It is the amount of energy needed to completely separate a nucleus into its component neutrons and protons.
The configurations of the potassium atom is 1s22 2s22 2p66 3s22 3p66 4s11. Which of the following statements about potassium is true?
Its electron charge distribution or probability density is spherically symmetric.
The electronic energy levels of a certain system are given by En = E1*n2, where n=1, 2, 3. Assume that transitions can occur between all levels. If one wanted to construct a laster from this system by pumping the n=1 to n=3 transition, which energy level or levels would have to be metastable?
N=2 only
Choose the incorrect statement.
Nearly the entire charge of any atom is concentrated in the nucleus and the charge of the electrons is almost negligible.
A coil is connected to a galvanometer, which can measure the current flowing through the coil. You are not allowed to connect a battery to this coil. Given a magnet, a battery and a long piece of wire. can you induce a steady current in that coil?
No, it is impossible to induce a steady current in the coil.
To sustain laster action it is usually necessary to place the lasing material between the 2 mirrors of an optical cavity. Why?
Photons are reflected back and forth through the lasing medium, which greatly increases the probability of stimulated emission.
Which of the following statements is false of total internal reflection (TIR)?
TIR causes a portion of the light to be refracted and the rest to be reflected
14C is produced in the upper atmosphere by cosmic rays. Living organisms uptake 14C. Assume we isolate the same quantity of 14C from a 1000 year old fossil and from a recently harvested tomato. We monitor the decay of these quantities.
The 2 samples will have approximately the same number of decays per second.
The cesium isotope 137Cs decays into the barium isotope 137Bs with a half-life of 30.2 years?
The atomic masses of cesium and barium are 136.9071 u and 136.9058 u. The decay is a beta minus decay. An electron is emitted.
To sustain laser action it is usually necessary to place the lasing material between the 2 mirrors of an optical cavity. Why?
The cavity recycles most of the photons and therefore increases the probability of duplication.
Violet light is able to eject electrons from the surface of potassium metal, whereas red light cannot. Why?
The frequency of red light is lower than that of violet light and its photon energy is not sufficient to eject electrons.
Consider a double slit interference experiment with electrons. What happens to the interference pattern if we increased the energy of the electrons?
The fringes get closer together
In the Compton effect, a photon of wavelength λ and frequency f hits an electron that is initially at rest. Which one of the following occurs as a result of the collision?
The photons lose energy, so the final photon has a wavelength > λ
A green and a red laster pointer each emit a 1 mW light beam. Which beam delivers more photons per second?
The red beam
For the electron in the hydrogen atom, which of the sets of the observables below are compatible?
The total energy, the magnitude of the orbital angular momentum and its component along the z-axis.
Does the wave function let us make predictions about the outcome of measurements?
The wave function lets us make predictions about the outcome of all measurements, but we have to operate on it with an operator corresponding to the measurement we want to make.
Can you take a picture of a virtual image with a camera?
Yes, the camera lens focuses light from a virtual image in exactly the way as light coming directly from an object
In a Compton scattering experiment, a beam of x-rays of wavelength 0.07 nm scatters of nearly free electrons. The scattered radiation is investigated as a function of the angle theta between it and the primary beam. The scattered radiation contains
a component shifted in wavelength by an amount that is independent of the wavelength of the primary beam.
The total energy of a particle is the sum of its kinetic energy and its potential energy. The zero of the potential energy can be chosen arbitrarily, so the potential energy can be negative. Classically forbidden regions are where
a particle's total energy is less than its potential energy
A hydrogen atom is in the third excited state. To what state should it jump to a) emit light with the longest possible wavelength? b) emit light with the shortest possible wavelength? c) absorb light with the longest possible wavelength?
a) n=3 b) n=1 c) n=5
Which of the following statements are true about the electric field? (a) The strength of the electric field created by an object A at a point P depends on the separation between A and P. (b) The strength of the electric field created by an object A at a point P depends on the net charge of object A. (c) The strength of the electric field created by an object A at a point P depends on the charge of the test object used to measure it. (d) The strength of the electric field created by an object A at a point P is the magnitude of the electric force per unit charge A exerts on a test charge placed at P.
a, b, d
Which of the following statements are true statements about the electric field? (a) The strength of the electric field created by an object A at a point P depends on the separation between A and P. (b) The strength of the electric field created by an object A at a point P depends on the net charge of object A. (c) The strength of the electric field created by an object A at a point P depends on the charge of the test object used to measure it. (d) The strength of the electric field created by an object A at a point P is the magnitude of the electric force per unit charge A exerts on a test charge placed at P.
a, b, d
3 pithballs are suspended from thin threads. Various objects are then rubbed against other objects (nylon against silk, glass against polyester, etc) and each of the pithballs is charged by touching them with one of these objects. In one set of experiments, it is found that pithballs 1 and 2 repel each other and that pthballs 2 and 3 repel each other. From this we can conclude that
all 3 carry charges of the same sign
Which of the following statements about interference in a Young's double slit experiments is true?
all are false
A bird is sitting on a perch peering into a small convex mirror on its cage. The image it sees is
always virtual
At what rate must Uranium 235 undergo fission by neutron bombardment to genereate energy at a rate of 100 W (1 W = 1J/s)? Assume each fission reaction relesases 220 MeV of energy.
approximately 3*10^12 fissions per second
Which of the diagrams represents resistors connected in series?
b only
If a light signal and a radio signal were emitted simultaneously from Alpha Centurai, which signal would reach the earth first?
both signals would arrive at the same time
Which of these elements is not produced by thermonuclear fusion processes in stellar interiors?
bromine
By what factor is the radius of the nucleus 160Dy bigger than that of 20Ne?
by a factor of 2
Consider a particle tunneling through a barrier. Which of the following will yield the maximum increase in the likelihood of tunneling? a. decrease the height of the barrier b. increase the width of the barrier c. increase the mass of the particle
decrease the height of the barrier
Electric fields are produced by: (a) distributions of separated charges. (b) steady currents in neutral wires. (c) changing magnetic fields.
distributions of separated charges and changing magnetic fields
A person who is near-sighted, or myopic, cannot focus on faraway objects (objects at infinity) because the curvature of the person's eye-lens is too great. This causes parallel rays (from a distant point source) to bend too much and focus in front of the retina. This person needs eyeglasses with lenses that are
diverging
Thru rubbing, an object has acquired a charge of -1 nanoCoulomb
electron has been transferred
You have just pulled your clothes from the dryer and find that a sock is clinging to your jeans with static electricity. You pull the 2 apart. As the jeans and the sock move apart, the force between them becomes weaker because the
force between the electric charges becomes weaker with increasing resistance
If you shoot a single photon through 2 slits to hit a screen it
has a chance of hitting anywhere on the screen, but on average a better chance at hitting where the interference pattern is brightest.
The initial fragments formed by fission
have more neutrons than protons.
Consider a photon hitting the screen to the left of center as in image. Which slit did it go thru?
impossible to know
A positive charge is moving with velocity v in a region with magnetic field B. What is the direction of the force on the particle?
into the page
2 stars that are close together are photographed thru a telescope. Which situation would result in the most clearly separated images of the stars?
large lens, blue stars
Which of the transitions below can produce a spectral line in the visible region of the emission spectrum of hydrogen?
n=4 to n=2
Heisenberg's uncertainty principle of quantum mechanics
none of the above
A material is known to be an isotope of lead, although the particular isotope is not known. From such limited information, which of the following quantities can you specify: its atomic number, its neutron number, its atomic mass number?
only its atomic number
The nuclear force is
short range and charge independent
Bohr's model of the atom accounted for the spectra of
single-electron atoms
Assume the voltage across the ends of a wire is doubled. If the material obeys Ohm's law, which one of the following statements concerning the resistance of the wire is true?
the resistance is not changed
Complete the following statement: An individual copper atom emits electromagnetic radiation with wavelengths that are
unique to all copper atoms
Which of the following best describes the image formed by a concave mirror when the object is located somewhere between the focal point (F) and the mirror surface?
virtual, upright, and reduced
The main difference between any radio wave and a light wave is it
wavelength
A magnet falls through a metal pipe. This induces a current which
will slow down the falling object
The white circles in the figure represent minima of the diffraction pattern formed when a bright point-source, for example a distant star, is viewed thru a small circular opening. In accordance with Rayleigh's criterion, the closest the central maximum of another point source could lie in this pattern and still be barely resolvable
would be at point B
An energy eigenfunction ψ (x) for an electron in the potential energy well pictured below is shown. Around which point is the electron most likely to be found?
x=D
The wave function ψ(x,t) for a neutron is shown at some time t. Around which point is the neutron most likely to be found at time t?
x=xc
Which statement is false? Quantum mechanics predicts that
you can never know the energy and the magnitude of the angular momentum exactly at the same time.
Identify in order the decay processes in the decay series shown below.
α, β-, β-, α
