Compare a matter waveo2o 2gpn l1pag*:p o3p $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory ba6 wjq7.. s0,yztwbiof the atom is not compatible with quantum mechanics, particulas7ti zj .bqaw.,0 wyb6rly the uncertainty principle.

Explain why it is that tkb tqga(, 0li)he more massive an object is, the easier it becomes to predict itst(gb )a,lk 0iq future position.

In view of the uncertainty principle, why does a baseball seem t7j pa63me15zil w 6kiqo have a well-defined position and speed whereas an electron does nki1ew aql p6 3z765mjiot?

  Would it ever be possible to balance a very sharp needl41r ,wpr6if mbbm.m o6e precisely on its point? Explainm or6pbf.rm,im w61b4.

  A cold thermometer is placed in a hot bowl of soup. Will the temperat*e f diw4l*qyi)eq)2dure reading of the thermometer be thed)fd* eq)* e2qyi4ilw same as the temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well yayz6lxn3 8-zt.wc3 jnou can make any single measurement of position?6lxw3 c3t-ynzn 8.jza

If you knew the position of an object precisely, with. ii2ko4oay j8y.,mvr no uncertainty, how well would you know its momentujkr ovmiy.8,4 y i2oa.m?

  When you check the pressure in a tire, doesn't some air inevitably escape? hc6*bw jp (+xyxqq67q- r8zmeIs it possible to avoid this 8 (-pyrj7z*qmxb6c wq+q6he x escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-f: qv f5;3rrqjstate energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in thqff53vj r;rq: eir values (an "energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, the Bohr model or the quantum-mechanica(t e,z65sl9bj;p cxnll model, predicts that the electron spe bps96xc;jl ,e(n5tlznds more time near the nucleus?

The size of atoms varies by 96 4ach:ccllo only a factor of three or so, from largest to smallest, yet the4a6cl9hco lc : number of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate ligj; daln+br/y v0vkuc( m4z:9 cht as they jump down tk clrbyv(z9 4jmua;:/d 0cnv+o the $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin but otherwis:8 1lmzw-g-qk,bx lipe quantum mechanics welb:ikg81wxq -mz - ,lpre valid? Consider the first 20 elements or so.

  Which of the followingszq ,c4bua :3ifl;a*8bwb z i3 electron configurations are not allowed:
(a) $1s^2\,2s^2\,2p^4\,3s^2\,4p^2$;  ----待选择----allowednot allowed 
(b) $1s^2\,2s^2\,2p^3\,3s^1$;  ----待选择----allowednot allowed 
(c) $1s^2\,2s^2\,2p^6\,3s^2\,3p^3\,4s^2\,4d^3\,4f^1$? ----待选择----allowednot allowed 
If not allowed, explain why.

Give the complete electron configuration for a uranium atom (caoykjp/); v0g 7mryl4 vreful scrutiny across the periodic table on the v 7yk4g0v/)yolp;rj minside back cover will provide useful hints).

In what column of the periodic table would you expect to fiexm(s*:xdtk lm 96r)vnd the atom with eachm9:s v * eklt6(drxmx) of the following configurations:
(a) $1s^22s^22p^63s^2$;
(b) $1s^22s^22p^63s^23p^6$;
(c) $1s^22s^22p^63s^23p^64s^1$;
(d) $1s^22s^22p^5$?

Why do chlorine and iodine exhibit similar prope ob kkbw(6+i)xrties?

Explain why potassium and sodium exhx-jxa,v + :avwibit similar properties.

The ionization energy for nenuscdj *cq8 ;:7vbagz36iek, on $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelength in (Fkjt )*/qi6 q;ehgsx 1oig. Below) imply a photon nature for light? ;jx1ego i)thqk/6*q s

Why do we not expect perfect agreement between measured values of X6gx2c-hz1nawa 4.58 ilhj qe jfsfe8 2-ray line wave clagxah6hw-n58jqfjfz2s8 1 e. i24 elengths and those calculated using Bohr theory?

How would you figure out which lines in tpyeidu2g/rm6 84br6 an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep withi6byv 9 a23uvezn an atom to produce shorter wavelengths than transitions by oeua bzvy3v9 26uter electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it thedg tcp)ep;yq9bb/q,1 same?

Explain how a 0.0005-W laser beam, photographed at -rso1bka bx +s5)w2 yva distance, can seem much stronger thax vbk5r o+sy2-1s )wban a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as the inverse square o7hb inq lws983eht -f7f the d 977hn itqslf8w3 -ebhistance? Explain. ----待选择----yesno 

  The neutrons in a parallel beajj1 n 8tc-) i4:ukroxhm, each having kinetic energy $0.40 \, \text{eV}$ are directed through two slits $0.50 \, \text{mm}$ apart. How far apart will the interference peaks be on a screen $1.0 \, \text{m}$ away? [Hint: First find the wavelength of the neutron.]
$\Delta y$ =    $ \times 10^{-7}\ \text{m}$

  Bullets of mass $3.0 \, \text{g}$ are fired in parallel paths with speeds of $220 \, \text{m/s}$ through a hole $3.0 \, \text{mm}$ in diameter. How far from the hole must you be to detect a $1.0 \, \text{cm}$-diameter spread in the beam of bullets? L =    $ \times 10^{28}\ \text{m}$

  A proton is traveling with a z5kw9 3tj v(5bn9 thoespeed of $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. With what maximum accuracy can its position be ascertained? [Hint: $\Delta p \approx m \Delta v$]
$\pm$    $ \times 10^{-11}\ \text{m}$

  If an electron’s position can be ; .mewvu 25eicmeasured to an accuracy of $1.0 \times 10^{-8} \, \text{m}$, how accurately can its speed be known?
$\Delta v $=    $\times 10^{3}\ \text{m/s}$

  An electron remains in an excited state of 3-/+n)lpgs1s+nixehv ung .man atom for typically $10^{-8} \, \text{s}$. What is the minimum uncertainty in the energy of the state (in eV)?
$\frac{\hbar}{\Delta t}$ =    $ \times 10^{-8}\ \text{eV}$

  The $Z^0$ boson, discovered in 1985, is the mediator of the weak nuclear force, and it typically decays very quickly. Its average rest energy is $91.19 \, \text{GeV}$, but its short lifetime shows up as an intrinsic width of $2.5 \, \text{GeV}$ (rest energy uncertainty). What is the lifetime of this particle?
$\frac{\hbar}{\Delta t}$=    $ \times 10^{-25}\ \text{s}$

  What is the uncertainty in the mar- *v :q*yna8dk/wyhzoaf) 2q ss of a muon $(m=105.7 \, \text{MeV/c}^2)$, specified in $\text{eV/c}^2$, given its lifetime of $2.20 \times 10^{-6} \, \text{s}$? [Hint: $\Delta E \approx \hbar / \Delta t$ and $\Delta m = \Delta E / c^2$]
$\frac{\hbar}{\Delta t}$=    $ \times 10^{-10}\ \text{eV}$
${\Delta m}$ =    = $\times 10^{-10}\ \text{eV}$

  A free neutron $(m=1.67 \times 10^{-27} \, \text{kg})$ has a mean life of $900 \, \text{s}$. What is the uncertainty in its mass (in kg)?
${\Delta m}$=    $\times 10^{-54}\ \text{kg}$

  An electron and a $140$-g baseball are each traveling $150 \, \text{m/s}$ measured to an accuracy of $0.055\%$. Calculate and compare the uncertainty in position of each.
For the electron $\frac{\hbar}{m\Delta v}$=    $\times 10^{-3}\ \text{m}$
For the baseball $\frac{\hbar}{m\Delta v}$ =    $ \times 10^{-33}\ \text{m}$

  Estimate the lowest possible energy of a4vxzx2qm;bil5q i: -a neutron contained in a typical nucleus of radiusx2-;5a: l bvm4qi zxqi $1.0 \times 10^{-15} \, \text{m}$. [Hint: A particle can have an energy at least as large as its uncertainty.]
$\frac{\hbar}{\Delta x} $=    $\times 10^{-19}\ \text{kg} \cdot \text{m/s}$
E =    Mev

  Use the uncertainty hc:yc* 5w nhv bcth /+t*ev7+uprinciple to show that if an electron were present in the nucl+ ech+ *vt 7huwc:ht /5bcvy*neus $(r \approx 10^{-15} \, \text{m})$, 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.) [Hint: A particle can have an energy at least as large as its uncertainty.]
E $\approx$    Mev

  How accurately can the pos7z3i)m- h ojvqyy) bq46ihy0l ition of a $3.00$-keV electron be measured assuming its energy is known to $1.00\%$?
$\frac{\hbar}{\Delta p} =$    $ \times 10^{-10}\ \text{m}$

  For $n=6$, what values can $l$ have?
$\ell$ =    or    or    or    or    or   

  For $n=5, l=3$, what are the possible values of $m_l$ and $m_s$?
$n_\ell$ = $\pm $    or $\pm $    or $\pm $    or $\pm $   
$m_s$ = $\pm $ 1/  

  How many electrons can be in fb6 lb:ay 36k.sd+blothe $n=6, l=3$ subshell?    elections

How many different states are possible for aj n7;9kw 5kkd uq-qfb7z.cmy,wd -x/kn electron whose principal quantum numkqzqc- ukdnk,j ym7fdb x957- ; ./wwkber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground st-x7um d0 ja r6 s+utm+/zmnj4date of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground szldq d a);r-thph ,+5rtate of nitrogen $(Z=7)$.

  Suppose a certain hyocqa7 q2bzwme8-- f 7sdrogen atom has $l=4$. What are the possible values for $n, m_l$, and $m_s$?
n $\ge $   
$m_\ell$ =    $\pm$    $\pm$    $\pm$    $\pm$   
$m_s$ = $\pm$   

  Calculate the magnitude of the angular momenth- +n2ug lns/gum of an electron in the $n=4, l=3$ state of hydrogen.
L =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  If a hydrogen atom haw ;h0ufm :m5tokyx/-ps $m_l=-3$, what are the possible values of $n, l$, and $m_s$?
$\ell \ge $   
n$\ge \ell$ +    (minimum 4)
$m_s$ = $\pm $   

  Show that there can b.0 dlu/ b e/p+yao/kove 18 electrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for element9 r ;;1t(qtttb0a7kac3ttw b js with $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electron configuhq 8hpwx0g zut88 6om;ration for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the perio zq 8hu o0pthx;m86wg8dic table inside the back cover.]

  A hydrogen atom is inx -o:gt+ , wehkog7gs3 the $6s$ state. Determine
(a) the principal quantum number, n =   
(b) the energy of the state, $E_6$ =    Mev
(c) the orbital angular momentum and its quantum number $l$ L =   
(d) the possible values for the magnetic quantum number.$m_\ell$ =   

  Estimate the binding energy of the third electron in lithium using tgwuuu op3 u-,g/ 66iavhe Bohr theory. [Hint: This el wgui aup6 u63ov-/gu,ectron has $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momentum is zero for a fiswue,)zc2g / n.xql*flled subshell.

  For each of the following atomic transitions, / 7k lf*ddcn4duqk azk3(f6 (cstate whether the transition is allowed or forbidden, and if forbidden, what rule is being vu7(k cn/4fcqk(3zlafdd 6dk* iolated:
(a) $3p \to 4p$  ----待选择----forbiddenallowed 
(b) $1s \to 2p$  ----待选择----forbiddenallowed 
(c) $3d \to 2d$;  ----待选择----forbiddenallowed 
(d) $4d \to 2p$;  ----待选择----forbiddenallowed 
(e) $4s \to 2p$. ----待选择----forbiddenallowed 

  An excited H atom is i7dkt*g n0p9 don a $6d$ state.
(a) Name all the states $(n, l)$ to which the atom is "allowed" to jump with the emission of a photon.
(b) How many different wavelengths are there (ignoring fine structure)?   

  What are the shortest-wavelength X-rays emitted b *3;o1d8chuqda xtsl*y electrons striking the face ooacx3l8 1u h*; ds*qtdf a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung 6r 2qfjyp93-d8 x vhvgg; l:dnX-rays emitted from an X-ray tube have vp- 8:y9g2rdl 6xfjh; dv3qgn$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wav5ejf6re 1 k msv5zc7*ielength $\lambda_0$ is given by $\lambda_0 = \frac{1240 \, \text{nm} \cdot \text{V}}{V}$ where $V$ is the X-ray tube voltage in volts.

  Estimate the X-ray wavelength emitted cx,p 6sbey9 r1when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for azd3s5ga5s:f f n $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estima3m7 chq 8n3ispte the wavelength for an $n=3$ to $n=1$ transition in molybdenum $(Z=42)$. The measured value is $0.063 \, \text{nm}$. Why do we not expect perfect agreement?
$\lambda $ =    nm
n =   

  A mixture of iron anx ctx i9rg08.pd an unknown material is bombarded with electrons. The wavelength of .xxc 098pgirt the $K_\alpha$ lines are $194 \, \text{pm}$ for iron and $229 \, \text{pm}$ for the unknown. What is the unknown material?
 ----待选择----copperironmagnesiumvanadiumchromiummanganese 

  A laser used to weld detached retin+(ijqg mqr7fo z:3;r4o ly8kz as 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?
E =    J
N =    $\times 10^{16}\ \text{photons}$

  A low-power laser used in a physics lab mighgm8 egu,eu/a*( c4jv kt have a power of $0.50 \, \text{mW}$ and a beam diameter of $3.0 \, \text{mm}$. Calculate
(a) the average light intensity of the laser beam, I =    $W/m^2$
(b) compare it to the intensity of a lightbulb producing $40$-W light viewed from $2.0 \, \text{m}$.I =    $W/m^2$ The laser beam is more intense by a factor of   

  Estimate the angular spread of a laser beam h*4o ej5cpm 1;nqb+ (g,rta5odug;xbdue to diffraction if the beam emerge,p5qg5ohtra *cg+ d;ne4o;ub xm jb (1s through a $3.0$-mm-diameter mirror. Assume that $\lambda = 694 \, \text{nm}$. What would be the diameter of this beam if it struck
$\theta$ =    $ \times 10^{-4}\ \text{rad}$
(a) a satellite $300 \, \text{km}$ above the Earth, D =   $ \times 10^{2}\ \text{m}$
(b) the Moon?D =   $ \times 10^{5}\ \text{m}$

  What is the wavelength of th0), )wlkbefuxe He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the p /8gb(p.h37el o wy0tv*iqodc.a du0nosition uncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 and assu(ou8nd.g yv 7d. *0lpc0 ohib eq/a3twme the momentum can be anywhere between this value and zero.] How does this result compare to the Bohr radius?

  An electron in the $n=2$ state of hydrogen remains there on average about $10^{-8} \, \text{s}$ before jumping to the $n=1$ state.
(a) Estimate the uncertainty in the energy of the $n=2$ state. $\frac{\hbar}{\Delta t} =$    $ \times 10^{-8}\ \text{eV}$
(b) What fraction of the transition energy is this? $\frac{\Delta E}{E} =$    $ \times 10^{-9}$
(c) What is the wavelength, and width (in nm), of this line in the spectrum of hydrogen?
$\lambda$ =    nm
$\Delta \lambda =$    $ \times 10^{-7}\ \text{nm}$

  What are the largest and smn r2.8cogr gr19o im:eallest possible values for the angular momentum $L$ of an electron in the $n=5$ shell?
$\text{The smallest value of } L \text{ is}$ =   
$\text{The largest value of } L \text{ is}$ =    $\times 10^{-34}\ \text{kg} \cdot \text{m}^2/\text{s}$

  Estimate
(a) the quantum number $l$ for the orbital angular momentum of the Earth about the Sun, $\ell$ =    $ \times 10^{74}$
(b) the number of possible orientations for the plane of Earth's orbit. N =    $ \times 10^{74}$

  A $12$-g bullet leaves a rifle at a speed of $180 \, \text{m/s}$.
(a) What is the wavelength of this bullet? $\lambda $ =    $ \times 10^{-34}\ \text{m}$
(b) If the position of the bullet is known to an accuracy of $0.60 \, \text{cm}$ (radius of the barrel), what is the minimum uncertainty in its momentum? $\frac{\hbar}{\Delta y}$ =    $\times 10^{-32}\ \text{kg} \cdot \text{m/s}$

  Using the Bohr formula for the radius of avmov: m .g5lv:l) n+bbn electron orbit, estimate the average distance from the nucleuv vnbgo +b:m. :vl5)lms 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?
$r_{\text{uranium}} =$    $ \times 10^{-13}\ \text{m}$
$\text{the binding energy is }$    $ \ \text{keV}$

  An X-ray tube operatesipk 1c..x x: )i6)hv q/nnqblw at $95 \, \text{kV}$ with a current of $25 \, \text{mA}$ and nearly all the electron energy goes into heat. If the specific heat of the $0.085$-kg plate is $0.11 \, \text{kcal/kg} \cdot ^\circ \text{C}$, what will be the temperature rise per minute if no cooling water is used?
$\frac{\Delta T}{t} =$    $ \times 10^{3}\ ^\circ\text{C}/\text{min}$

  The ionization (binding) energy of the outermost el79gym6e9it lyectron in boron is $8.26 \, \text{eV}$.
(a) Use the Bohr model to estimate the "effective charge," $Z_{\text{eff}}$, seen by this electron. $Z_{\text{eff}} $=   
(b) Estimate the average orbital radius. z =    $ \times 10^{-10}\ \text{m}$

  Use the Bohr theory to show that the Moseley plot(F-96r2 o iw fh(fdpg2tpig. Below) can be written $\sqrt{\frac{1}{\lambda}} = a(Z - b)$, where $b \approx 1$, and evaluate $a$. a =    $\ \text{m}^{-\frac{1}{2}}$

(a) Show that the number of different aqz ycwz)0bn;5 r2vgs2,kqjxh *tp; 3states 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 states65 qarag 1k: 1:dgieele+k+os possible for a given value of gqo k5eee+6 id1r :gl+sa:ka1$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot throu/s6z3 vkkqc/mgh two narrow slits in a barrier. The slits are a cm sv 6z/k3/kqdistance $2.0\times10^{-6}\ \text{m}$ apart. If a screen is placed 35.0 cm behind the barrier, calculate the spacing between the "bright" fringes of the interference pattern produced on the screen. $\Delta y =$    $\ \mu\text{m}$

  The angular momentum in the hydrogen atom is given both by the Bohr model6+w./ryjkgg ddel:-2 rc* y dp and by quantum mechanics. Comp ydrj c6g -.dpke:dr+*yw lg2/are the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a9)y7q-;x vc 5pmi tbca speed of $(22 \pm 0.22)\ \text{m/s}$. With what maximum accuracy can its position be determined? $\Delta x =$    $\times 10^{-37}\ \text{m}$

  An atomic spectrum containsw.(rl37 bpi.giw1t d z a line with a wavelength centered at 488 nm. Careful meas3p gbl(.ridiw z7 1tw.urements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest on 31wilb 9; j-aduzb4vy9s66ft rpw. across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a scree tjzru49b16dbyaopli w v3 s-f69 .n;wn 28 m away? $\Delta y$ =    nm

An electron and a protoy(s/:ns6.h, ef fwmw)uuj: mzn, 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 raw: m6wu.:n fujs( )smf /hezy,tio of the uncertainty in their momentum.

  If the principal quantu5 l -q0ys*tfgym number n were limited to the range from 1 to 6, how many ele*-tf 5gls yq0yments would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be movinx8(w/m u,+g aknrofo.g if your mass is 75.0 kf gr n8ow kxo/m,u.+(ag? $v = $    $ \times 10^{-35}\ \text{m/s}$
Would you notice diffraction effects as you walk through a doorway?  ----待选择----yesno 
Approximately how long would it take you to walk through the doorway?$\Delta t \approx $    $ \times 10^{34}\ \text{s}$

  Suppose that the spectrum of 5h-t v xj5.bj-uhufm*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 el ht*- h fjvju.x-55mubement is an ion with Z protons and one electron, determine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from tu i1* dj x d:77 ;y och*j8i1tkm7iyoomm//xgnhe surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength coroo*yyci*hn1u ;jmid/gx1xd i8j7:7m/ m7t okresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a laser be)vnyws+ -xp0e am, $$\theta \approx \lambda/D$$ , is precisely what you might expect from the uncertainty principle. [Hint: Since the beam's width is constrained by the dimension of the aperture D, the component of the light's momentum perpendicular to the laser axis is uncertain.]