PHYS 222 Exam 3
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 loses energy, so the final photon has a wavelength > λ
What is the wavelength (in nm) of a photon with energy E = 1.88 eV?
Use E=hv and then c=λv c=3x10^8ms- h=6.626x10^-34J E=1.88eV, 1.88eV=3.012x10^-19J E=hv: (3.012x10^19J)=(6.626x10^-34J)(v) v=4.546x10^14s- c=λv: 3x10^8ms-=(λ)(4.546x10^14s-) λ=6.59x10^-7m λ=660 nm or E = h*c /λ. (3.012*10^-19J)=((6.63*10^-34J)(3*10^8))/λ. Then *10^9 for nm. 1eV=(1.6*10^-19J).
In 5731 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?
(1/16)(½) = (¼) → (¼)(½) = (½) (5731)(½) = 2865.5 → (2865.5)(½) = 1432.75 = 1433
Electrons are ejected from a metal surface with energies ranging up to 0.5 eV when light with a wavelength of 356 nm is used. What is the work function of the metal in units of eV?
(1240/λ)-k k= 0.5 (1240/356)-0.5
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, and (c) absorb light with the longest possible wavelength?
(a) n = 3 (b) n = 1 (c) n = 5
16 8O, 17 8O, and 18 8O are all stable oxygen isotopes. Which one likely has the largest binding energy per nucleon?
16 8O because it is doubly magic.
A thin film of oil (n = 1.52) is located on a smooth, wet pavement. When viewed perpendicular to the pavement, it appears to be predominantly red (618 nm). What is the minimum thickness of the oil film in nm? Enter a number with one digit behind the decimal point.
2nt=(m+(1/2))*λ n=refractive index t=thickness m= integer λ= wavelength For minimum thickness, m=0 2nt=(0+(1/2))*λ t = ((0+(1/2))*λ) / (2n) -----> t=(λ)/(4n) n=1.52 (2)(1.52)t = (0+0.5)*(618 nm) t=101.6 nm
A hypothetical atom has 3 energy states. Assuming all transitions are possible, how many spectral lines can this atom produce?
3
Photons with λ = 250 nm (hf = 5.0 eV) hit a metal surface and emit photoelectrons with a maximum kinetic energy Eelectron = 2.0 eV. What is the work function of the metal?
3 eV
Which of the following (n, ℓ, mℓ, ms) combinations is impossible for an electron in an hydrogen atom?
3, 1, -2, ½
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
For a grating, interference maxima are observed at angles θ, for which d sinθ = mλ. If a grating has 2500 grooves per cm, what is d?
4 micrometer
What wavelength monochromatic source in the visible region (390 to 710 nm) can be used to constructively reflect off a coating on glass (n = 1.46), if the coating is 150 nm thick?
438 nm
Two parallel light rays, initially in phase and having a 500 nm wavelength, reach a detector after one of the rays travels through a 10 cm long block of glass with an index of refraction of 1.5, while the other ray stays in air. The optical path difference between the two rays at the detector is __?
5 cm
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 m = 0?
6
)A hydrogenic ion with Z = 22 is excited from its ground state to the state with n = 7. How much energy (in eV) must be absorbed by the ion? Enter a number with one decimal place after the decimal point.
A hydrogenic ion with Z = 27 Z=26 n=9 is excited from its ground state to the state with n = 10. How much energy (in eV) must be absorbed by the ion? E2=(-27^2*(13.6eV/(10^2))= -99.144 E1=(-27^2*(13.6eV/(1^2))= -9914.4 99.144-9914.4= 9815.256= 9815.3
What are the changes in the mass number A and the atomic number Z of a nucleus that undergoes β+ 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 of these elements is not produced by thermonuclear fusion processes in stellar interiors?
Bromine
What is the first element in the periodic table to have a filled 4s subshell?
Ca
The blue tint of a coated camera lens is largely caused by what effect?
Interference
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
What does observing a double slit interference pattern with light suggest to us?
Light behaves like a wave.
A radioactive substance has a mean-life τ of 16 years. Assume we start with 166 kg of the substance. How many kg of the substance will be left after 27 years? Enter a number with one digit after the decimal point. Lowercase e^x is a button on the calculator.
m=mo*e^(-t/T). m=166[e^(-27/16)]=30.7kg.
Which of the transitions below can produce a spectral line in the visible region of the emission spectrum of hydrogen?
n = 4 n = 2
At what rate must Uranium 235 undergo fission by neutron bombardment to generate energy at a rate of 434 W (1W = 1J/s)? Assume each fission reaction releases 200 MeV of energy. Enter the number of fissions/s
n= 434 J / 3.2044 x 10-11 J = 1.35438772 x 1013 The number of fissions/s = 135
The middle of the first order maximum, adjacent to the central bright fringe in a double-slit experiment, corresponds to a point where the optical path length difference from the two slits is equal to ...
one wavelength.
A beam of light A has twice the wavelength but the same intensity as a beam B. The number of photons that hit a given area in a given time, when illuminated by beam B is...
one-half the number that hit when the area is illuminated by beam A
What is the deBroglie wavelength (in nm) of a neutron (m = 1.67*10-27 kg) moving with a speed of 24 m/s?
p=h/wavelength p=mass of particle x speed of particle (m x v) h=planck (6.626e-34) p=1.67e-27 x 89 p= 1.4863e-25 Wavelength = 6.626e-34/1.4863e-25 = 4.458e-9 meters x 10^9 =4.46 nm
The nuclear force is.....
short range and charge independent
Bohr's model of the atom accounted for the spectra of
single-electron atoms.
Light from an argon laser strikes a diffraction grating that has 4223 lines per cm. The central and first-order principal maxima are separated by 0.5 m on a wall 1.55 m from the grating. What is the wavelength of the laser light in nm?
tan-1= (.488/1.72) = 15.84 sin(15.84)x(0.01/5310) = 5.14 x 10-7
If the wavelength of the light were changed, and red light were passed through the slit,.....
the central bright region would become wider.
When a car is 500 m ahead of you, you see its tail lights as one long, red light. When the car is 100 m ahead of you, you see that the tail lights are actually several red lights placed close to each other. This is because
the pupil of your eye has a finite size.
Complete the following statement: An individual copper atom emits electromagnetic radiation with wavelengths that are
unique to all copper atoms.
Laser light (λ = 620.9 nm) is incident on a single slit. What is the maximum width of the slit (in nm) for which no diffraction minima are observed? Round to the closest integer.
wsinθ = kλ For k = 1, sinθ = λ/w If sinθ >= 1, or λ/w >= 1, or w <= λ, no diffraction, Therefore, the maximum width, w = λ = 620.9 nm Integer= 621 nm
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
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.
The angular separation of the two components of a double star is 0.4 microradians, and the light from the double star has a wavelength of 544 nm. What is the diameter (in cm) of the smallest telescope mirror that will resolve the double star?
θmin=(1.22*λ) /d λ= 544 nm d=diameter (find d) θ= angular separation (in radians, rad) 0.4µrad= 4.0x10^-6 rad d = ((1.22*(544x10^-9nm))/(.4x10^-6rad) d = 165cm
It is necessary to coat a glass lens with a nonreflecting layer. If the wavelength of the light in the coating is λ, the best choice is a layer of material having an index of refraction between those of glass and air and a thickness of ___?
λ/4
Light of wavelength λ1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to λ2, the fringes move closer together. What is the relationship between λ1 and λ2.
λ1 is larger than λ2.
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
On a balance scale, you put 2 neutrons and 1 proton on one side and you put a tritium nucleus (3H) on the other. Which side weighs more?
. The two neutrons and 1 proton.
A stream of electrons is of energy E is incident on a potential barrier of height U and thickness d. Even though U >> E, 5% of the electrons tunnel through the barrier. If the thickness of the barrier decrease to 0.16 d, what percentage of the electrons will tunnel through?
0.05^0.86 = 0.076 Answer is 7.6 or 0.05^0.16=0.619 Answer is 61.9=62.
A gamma ray photon has an energy of 1.07 GeV. (1 GeV = 109 eV.) What is the wavelength of the gamma ray in fm? (1 fm = 10-15 m)? Enter a number with 2 digits behind the decimal point.
1.16 (6.63*10^-34)(3*10^8)/ (1.07*10^9* 1.60*10^-19)
An electron in a hydrogen atom makes a transition from the n = 36 to the n = 3 energy state. Determine the wavelength of the emitted photon (in nm). R is a constant.
1/λ=R((1/(n^2 final ))-(1/n^2 inital)) 1/λ=1.097*10^7m^-1*((1/(3^2))-(1/(36^2)) 1/λ= 1210424.383m^-1 λ=1/1210424.383m^-1= 8.26E-7 m= 826 nm
The radius of an atomic nucleus is of the order of
10^-15 m
The half-life of 14C is 5730 years. Suppose an ancient bone is found in which the ratio of 14C/12C is ¼ that found in the atmosphere and in living plants and animals. Approximately how old is the bone?
12000 years
You have 16 kg of a radioactive sample with a certain half-life of 15 years. How much is left after 60 years?
1kg
Which of the following condensed notations gives the lowest energy electronic configuration for doubly ionized Magnesium (Mg)?
1s^2,2s^2,2p^6
If the orbital angular momentum is l = 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 ħ?\
2. 4.47 4
Choose the incorrect statement. 1. Nearly the entire mass of any atom is concentrated in the nucleus and the mass of the electrons is almost negligible. 2. Nearly the entire charge of any atom is concentrated in the nucleus and the charge of the electrons is almost negligible. 3. The planetary model of the atom is wrong. Electrons do not have welldefined orbits. 4. Atoms are mostly empty space. The radius of the nucleus is ~10-5 times that of an atom and electrons seem to be point particles.
2. Nearly the entire charge of any atom is concentrated in the nucleus and the charge of the electrons is almost negligible.
Each proton-proton cycle generates 26.7 MeV of energy. If 2.7 Watts are generated via by the proton-proton cycle, how many neutrinos are produced?
2.7 J/(26.7 *(1.6*10^-13))= 6.32*10^11 2*(6.32*10^11)= 1.26*10^12
222Rn (Radon) is an unstable nucleus which alpha decays. The resulting nucleus is
218Po
The isotope 234,92U undergoes five 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
A telescope with a 6 m diameter lens is in orbit around Earth. What is its maximum resolution for 400 nm light, i.e. what is the smallest angle θ(rad) between objects it just can resolve?
8.13*10-8
If the orbital angular momentum is l = 4, how many different projections along the z-axis are possible?
9
Which of the two series of pictures has the diffraction pattern correctly paired with the corresponding slits?
A
Which of the statements below is true?
Consider the photoelectric effect. The greater the work function of the target, the greater is the cutoff frequency
A hydrogen atom electron is excited to an energy of −13.6/4 eV. How many different quantum states are there with this energy?
Find n, find all possible l, for each l, find all possible m and ms. 8
Assume that in an atom the subshell n = 7, l = 1 is completely filled. How many electrons does this subshell hold?
For n=6 and l=0, the answer is 2. I used this: if l=0, the atom must be in s-block, which means m=0, so there's only one orbital possible. And there are two electrons per orbital, so 1x2=2.
Electrons with energy of 25 eV have a wavelength of ~0.25 nm. If we send these electrons through the same two slits (d = 0.40 mm) we use to produce a visible light interference pattern what is the spacing (in micrometer) between maxima on a screen 3.5 m away?
H=[(3.5m)(1)(0.25nm)]/(0.4mm) H=2.1875µm
Consider a double slit interference experiment with electrons. What happens to the interference pattern if we increased the energy of the electrons?
Hint: d sinθ = mλ, m = 0, 1, 2, ... . λ = h/√(2mE) The fringes get closer together
The electronic energy level 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 laser 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
What is a requirement for any nuclear chain reaction?
Neutron induced fission which releases more neutrons.
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
1/λ=R((1/(n^2 final ))-(1/n^2 inital)) 1/λ=1.097*10^7m^-1*((1/(3^2))-(1/(36^2)) 1/λ= 1210424.383m^-1 λ=1/1210424.383m^-1= 8.26E-7 m= 826 nm
Photons are reflected back and forth through the lasing medium, which greatly increases the probability of stimulated emission.
A laser emits photons continuously at a rate of 8.8*1016/s. If the wavelength of the photons is 632 nm, what is the laser power in mW?
Power= energy/sec = J/s Photon energy= hf= hc/wavelength # of photons/sec = power/ photon energy= rate of emission Photon Energy= (6.63*10^-34 J*s * 3*10^8 ms^-1)/ 6.32*10^-7 m= 3.147*10^-19 J This should be ignored. It is part of the units and not the equation. Power/3.147*10^-19J= 8.8*10^16s^-1 Power= 8.8*10^16s^-1 * 3.147*10^-19J= .02769 W = 27.69 mW
The figure below shows a red line and a green line of the same order in the pattern produced by a diffraction grating. If we increased the grating spacing d, would the lines shift to the right, shift to the left, or remain in place.
The lines would shift to the right.
A screen is placed 35 cm from a single slit which is illuminated with 559 nm light. If the distance from the central maximum to the first minimum of the diffraction pattern is 2.6 mm, how wide is the slit in micrometer?
R = 35 cm = 0.35 m lamda = 559 nm = 559*10^-9 distance from central maximum ti first minimum, y1 = 2.6 mm = 2.6*10^-6 let d is the slit width. we know, y1 = lamda*R/d ==> d = lamda*R/y1 = 559*10^-9*0.35/(2.6*10^-3) = 7.53*10^-5 m = 75.3 micro m
The long-range electrostatic repulsion between protons limits the size of stable nuclei. Why are there no large nuclei consisting only of neutrons, which do not repel each other?
The Pauli exclusion principle would require the neutrons to occupy very high energy states, yielding the nucleus unstable.
To sustain laser action it is usually necessary to place the lasing material between the two mirrors of an optical cavity. Why?
The cavity recycles most of the photons and therefore increases the probability of duplication.
How does the total mass of the fission fragments compare to the mass of the original nucleus in a fission reaction?
The fission fragments have less mass than the original nucleus.
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
A beam of green light is diffracted by a slit of width 0.55 mm. The diffraction pattern forms on a wall 2.06 m beyond the slit. The distance between the positions of zero intensity on both sides of the central bright fringe is 4.1 mm. What is the wavelength of the laser light in nm? Enter an integer.
d sinθ = m λ sinθ= z/L 547nm y = 2 * wavelength * D/d 4.1 *10^-3 = 2 * wavelength * 2.06/(0.55 *10^-3) solving for wavelength wavelength = 5.473 *10^-7 m = 547 nm
A green and a red laser pointer each emit a 1 mW light beam. Which beam delivers more photons per second?
The red beam
Why does a soap bubble reflect virtually no light just before it bursts?
The reflected light from the front and back surface destructively interfere, because the path difference is nearly zero, but the phase shift upon reflection differs by 180o for the two surfaces.
For the electron in the hydrogen atom, which of the sets of observables below are compatible observables?
The total energy, the magnitude of the orbital angular momentum and its component along the z-axis
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 two samples will have approximately the same number of decays per second.
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.
The figure shows two single-slit diffraction patterns. The distance between the slit and the viewing screen is the same in both cases. Which of the following could be true?
The wavelengths are the same for both. The width of slit 1 is larger than the width of slit 2.
The most stable nuclei all have around 60 nucleons. Why?
They have a diameter about equal to the range of the nuclear force.
A laser beam is used to read the information on an optical disc. In order to get more information on the disc, the wavelength of the laser used to read the information should be
decreased.
Consider a particle tunneling through a barrier. Which of the following will yield the maximum increase in the likelihood of tunneling?
do (A) only
Heisenberg's Uncertainty Principle of quantum mechanics....
does none of the above.
The interference pattern from two closely spaced slits can only is only produced if single slit diffraction spreads out the light. The graph below shows a double slit interference pattern. The ideal two-slit intensity pattern is multiplied by intensity of the single slit diffraction pattern. If this pattern was obtained with two slits spaced by d = 0.1 mm, what was the slit width w?
W=d/4
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
Assume that you observe a double-slit interference pattern with many fringes on a screen. The width of one of the slits is then halved, while everything else in the setup stays the same. Do you still observe the interference pattern on the screen?
Yes, but the contrast between the maxima and minima decreases.
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
Diffraction is the tendency of light to...
bend around corners and edges.
The cesium isotope 137Cs decays into the barium isotope 137Ba 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.
A Young's double-slit interference experiment is performed with monochromatic light. The separation between the slits is 0.35 mm. The interference pattern on the screen 3.5 m away shows the first maximum 5.8 mm from the center of the pattern. What is the wavelength of the light in nm? Enter an integer.
d sin θ = mλ d ( y/L) = mλ therefore λ = d ( y/L) / m (.35*10^-3m)[(5.8*10^-3m)/(3.5)]/1m= (5.8*10^-7) (5.8*10^-7)*10^9= 580 nm
A radioactive atom X emits a β+ particle. The resulting atom
has a atomic number that is one less than that of X.
If you shoot a single photon through two 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
The resolving power or resolution of a telescope is improved by using...
larger diameter telescopes objectives & shorter wavelengths.
