Compare a matter wav( 0ady. rvoi1c20n0 mrw6wwyre $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's t/v-p u+abn d0pheory of the atom is not compatible with quantum mechanics, particularly the uncertaintynpa/0vp ud+-b principle.

Explain why it is that the more massive an object is, the easier it becomes to p5/f (zf:+frekm gv4 gbredict its future pof/ 4eg(g +r5mf zkfb:vsition.

In view of the uncertainkc,iwas5 ,tc q+ek, k8 7lrie7ty principle, why does a baseball seem to have a well-de7cq, i,5+r8l we7sik,ketkca fined position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle preciselq)p vhjul0a 2:+50u;ll yohqay on its point? Expl up):ahvq5oulq0j lh0yl+a;2ain.

  A cold thermometer is placed in a hot bowl of soup. Will the temperatxs xg5-*w;tv5cpz,h dure reading of the thermometer be the same as tht xs 5-c xp*dvw,5ghz;e temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to hogd q*:/g6 ryivw well you can make any single measur/d:*yqr v6 iggement of position?

If you knew the position of an object precisely, with no uncertainty, how we1 j*gh p,;tddqll would you kno1;td*jg,q hdp w its momentum?

  When you check the pressure in a tire, doesn't some air inevitably escapeoabq q+hixcb9e.i-,* ? Is it possible to avoid this escape of air altogether? What is the relation to the uncertainty-*qobq9hia+ b.cix ,e principle?

  It has been said that the ground-state enepuz0vx),ywf- f2rqz+rgy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its energy z0wv2+ q rf)-zxyuf ,pform? Explain.

Which model of the hydrogen atom, the Bohr model or the quantum-meytinmu5 d8/f; chanical model, predicts that tdtui8 ; /5ymfnhe electron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, from larges6mgbga : ct,fh4pb8( rt to smallest, yet the number of electrons8cgb m6h,:t (gfb4 pra varies from one to over 100. Explain.

Excited hydrogen and excited helium a7bkby a -z),2tou wl;etoms both radiate light as they jump down to the2ku ,zbablytwe 7-; o) $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron8dg3adhau l/,26zbw gznz2 x2 spin but otherwise quantum mechazw,6a 3g/ d zglxz8ub22hdan2nics were valid? Consider the first 20 elements or so.

  Which of the following electron configurations ajgdo vt 0,x 7gbz6)atis 13;qk n2jh8tre 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 (cauiqby+r955lohvih+*8 -phm w reful scrutiny across the periodic table on the inside back cover will prowyu *9hq+rm +ob vi-h5ilp h85vide useful hints).

In what column of the periodic ta * zxswn(j2bq4ble would you expect to find the atom with each ofb q*wx( 2znsj4 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 properties?qwo(nfy6mep; c7:g5v

Explain why potassium and sodium exhibit similar 4-wpwz:ahj( 1xv 5wy) nv7owc2bjl 6wproperties.

The ionization energy for neon ; 8gg /y gspa3f0b6dz dow4py1$(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wudu8sf xgcx *8ep1 ,rgk a5f79avelength in (Fig. Below) imply a photon nature for light? 8 57x 1*sdpg rauf8c feu9xk,g

Why do we not expect perfect agreement between measured values of X-ray linlkishc*3)phs;,iq 1 f u/ gqk1e wavelengths and those calculated using )c gfss;3 kk u1hqi1/lihq,*p Bohr theory?

How would you figure out which lines in an X-ray spectrug/ ocdh5pfff /1,j ja;m correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep wa8szloo rbe* yls5 b,mor4 0l2rv(8 j+ithin an atom to produce shorter wavelengths than transitions by out8vm+ y o*r8 l40bsll(er b,jzo ar25soer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ fromnq4l o 1ajltm+ a+b7srn:w,5n ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographedccets p7j,+* j at a distance, can seem much stronger than a 1000-W street lam7*c js,+ejtp cp at the same distance.

  Does the intensity of light fro m1+ksg.f3)rmwes* k xm a laser fall off as the inverse square of the distance? Exkg smm. ksr13)e +wfx*plain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kineaca(.2sd +abppg3 o i,tic 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 speed ofm tz*+ merdfx- /n2i/b $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. 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 measured to an accuracymf959wuzfj-3 v jz;tm 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 :yy /bgw367ly hcr k+eof an 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 iufn njx rm1nx0faqk:5npyv s;+85 o- .n the mass 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 cr. ;ego;wi1bw3lkd 5of a neutron contained in a typical nucleus of d o;3k1;wwe l b.rigc5radius $1.0 \times 10^{-15} \, \text{m}$. [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 principfxpmk); ng :*tk fcg1+le to show that if an electron were present in the nucleumpkc+;g kffgx )t*n :1s $(r \approx 10^{-15} \, \text{m})$, 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 position of a 25wzvye h )d7l$3.00$-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 ov9 )o4gilyk (in the $n=6, l=3$ subshell?    elections

How many different states are moa) d l:26h lg/(zkyopossible for an electron whose principal quantum numbe z/ll): 2 k6y(modhogar is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the gfsu yoz*;17)u;hcvc6 d7e8 p jiwk*xkround state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers fo2,rvy 9 u wc31f4lmrdnh3f4u fr each electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrog55.o.nvd c/xql b66rzox21k av5zf rien 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 angu32x-m6re o:ml huolx4lar momentum 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 hn4o bb62/ zc+bsi ruj : r;l)ok4gkyi2as $m_l=-3$, 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 be 18 electrons in a "g" s( hms* 83e hjqkeu9 g(5rhk7ekubshell.    electrons

What is the full electron con84 8ocht0r n- cppixy5d )kb-guu1gu 2g5w3qhfiguration in the ground state for elements with $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electron configuration for (a) +qo(32 hkpetihia +hc ,8mpt*selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the p qptakmi3hh*,c e2 pho8 i(+t+eriodic table inside the back cover.]

  A hydrogen atom is in :jy: k t 7vtgtaf(d(n7 y,hov5the $6s$ 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 thkahal9;b : f mrt/dj-f.+w e8eird electron in lithium using the Bohr theory. [Hint: Tt-m /. de9r ;+lw:bhkj8affaehis electron 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 fk- r);5 xrblfgor a filled subshell.

  For each of the following aivbb;qa4a920d7 gcv gtomic transitions, state whether the transition is allowed or forbbv ag70ga;qb2cdi 94 vidden, and if forbidden, what rule is being violated:
(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 in4iwhk ki. ka:/ 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-wavew 5*j9+qz3.kjkze aculength X-rays emitted by electrons striking the face of w 9e*uc5kja+z. jkq3za $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremhn a:5wwyn3hy,+)z8 wckb 0 vxsstrahlung X-rays emitted from an X-ray tube have:w0, 8bk5v )y chwn3xhz+nyaw $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelu* ++aszes6 gpength $\lambda_0$ 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 wu .kd da5a if+ty+k hnhf6)2i7avelength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for grnf;;e5hv9m an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate th :b4q2p3baqdgr*0 ;h 7kjdttie 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 and an unknown material is bombardedn 4 qu7q.hq2 ;4dps *xebrfok5 with electrons. The wavelen pnsd qxq b4e*7rq4o 5.kf;2uhgth of 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 nqfp (.h1+..jpio nxgi+i6dwdetached retinas 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 usedaflnq0l/jl 7q.z d.w- in a physics lab might 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 due to 2hafuws350r)+4 o hjv8aoa* fldbnd3 diffraction if the beam emerges thr )3f ad2d3 v40b8ljwh5ahu ofasr+o*nough 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 o* j 65g/q.wyn 1sn gw-9xwgksff the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty fh4ig: (ow9zzc or the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 andzoz4:(h ig9c w assume 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 smallest possible values 6amk9;yvsf8s 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 an euhnotj(9 l2f-lectron orbit, estimate the average distance from the nucleus for an electrjhlt2 fuo 9-n(on 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 operate z slqf4,jbat 86itl qy1;x8.ds 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 outermosk9v 2ag - nmcd4eueedsk( m5-1t electron 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 Moseleu s0wf )llfuh+5m4.qsy plot(Fig. 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 ofjy i7w+js-f* l1nm2 mg different states 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 st p qeb5el6he:6qi0a d7rixc,,ates possible for a given value of hrei0qc5di a76 eb,q l :xep,6$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot throume0gt u4 3 vpm/yxo2-rgh two narrow slits in a barrier. The slits are a distanc2 -vtm4 x3o0/emguypre $2.0\times10^{-6}\ \text{m}$ 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 jjwaga:q2)8 iatom is given both by the Bohr model and by quantum mechanics. Com2gij8wja)q a:pare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling wit )-yp zudki*a,h a 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 contaieb0w53 .eph1 t7e (szwkzv 3dtv-8 prrns a line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the ee pk 3z1.srp0 vr8bh5wv- dw( e7etzt3xcited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest across 550 V. They are te,/nder+. h zwhen directed at two slits 0.70 mm apart. How far apart will the ie/ . ez,hwn+rdnterference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, eaowo2gmqfgo r 6y9(6v6ejn;+ 4 d6oi whch initially at rest, are accelerated across the same voltagim 6gvo6rwqf9e 4+o n6go;wjdhy2 (6oe. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum numnm3 9 k;ax g:c:cieuo6t7 s 7ie4/gcqjber n were limited to the range from 1 to 6, how many elements would we find in naturemet9 j ;s73 7xck: qceagu:i6c o4n/gi?   

  If your de Broglie wavelength were 0.50 m, how fast ww.lbt8 (ekg8vqf cd zt8z+o8 )ould you be moving if your m+efbc8( gtzl88o 8q.ktzwd v)ass is 75.0 kg? $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 an unknown el waa cl)r14/qw0zohc2ement shows a series of lines with one out of every four matching a line from the Lyman series of hydroa)azohq42l wc 1r 0/wcgen. Assuming that the unknown element 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 the surf:2u d7uh :e0lnro)ir tace of a certain metal when it is botro7iedu l)02rh:u n: mbarded with high energy radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a laser beam, dx:k wfzl-( z+$$\theta \approx \lambda/D$$ , 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.]