Compare a matter waver0w (bgr0biq8 $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the atom is not comp y e*cj836).gqsdv,yadgk yj )atible with quantum mechanics, particularly the uncertai. c8*jdg3,vg)y dyjs )q6ekaynty principle.

Explain why it is that the more massive an object is, the easie;mb oxgy61d ht4br2e( r it becomes to predict its futu tbyde;xor4g2 hm1b(6 re position.

In view of the uncertainty -ui-vdsp trmewz . r916ec 4k)principle, why does a baseball seem to have a well-defined.rct491 p wm6) z-k-udsveer i position and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precis3 qa0j*yxcz60x3om /h iilw)oely on its point? Exp * aw l6zyxmcxo/0ij30ihqo3) lain.

  A cold thermometer is placed in a hot bowl of soup. Will th(zdi bt zmf 21f*lg0j4e temperature reading of the thermometer be the same as the temperature of the hot soup before the measure (4 d1jbzitgm*ffz0 l2ment was made? Explain.

  Does the uncertainty principle set a limit to how well you can make an,k 2.yqecb . 8rmkqga4y single measurement omcqb8ya.2erg .q, kk 4f position?

If you knew the position of an object precisely, nt: j f(16v1i9ejyzpewith no uncertainty, how well would(ijpef11t6 nv z9 :ejy you know its momentum?

  When you check the pressure in a tire, doesn't some air indk 3wm.npz5o8 evitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertdpo8znw 5 km3.ainty principle?

  It has been said that the ground-state energy in the hydrogen atom can be n65a;i ekm6wf83odvg b.- wocprecisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the und8;k-iof 5bmna6wvgo.36ew c certainty principle in its energy form? Explain.

Which model of the hydrogen atom, the Bohr model or the quantum-mechanical ,bhncuii7.,sj773 4os jkgw m model, predicts that the electron spends more time near the nuclwk.sg,3i77j4shn bi, omc7 ujeus?

The size of atoms varies by only a factor of three or so, fr123 hbxgx- ajmom largest to smallest, yet the number of electrons varies from one 3baxgm2 jh-x1to over 100. Explain.

Excited hydrogen and excited helium atoms both ra gnjoiy y 8;921*fzxji;ak+akdiate light as they jump down to th;a+i *ygknj29a jki8z ofy;x 1e $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no n (6:hgnzyo j sbi*o4;8ek3yu electron spin but otherwise quantum mechanics were valid? Consider the first 20 elements orjs;:ynh zk6*og3 (o yu8be4in so.

  Which of the following*8 +6jxd/+n-c m orw)ckcgyem 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 urj( nphlh s28f/tq3l- zanium atom (careful scrutiny across the periodic 2 8/-j l(fszphhln3q ttable on the inside back cover will provide useful hints).

In what column of the perioczefdcu76+64 dsml mn7; jy7bdic table would you expect to find the atom with each of the followif+4zcb d7y7n mml676sde u c;jng 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 pr(21 kso vd1 .oxsfb3fboperties?

Explain why potassium and sodium exhibit similar propertieq h1hela2 g01bs.

The ionization energy for neoqmte/h.k wv:v n3 t:w3n $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelength in (Fig. Below) imply a photon nature 4edkh+bq jw+9iokw1 ( for light? d9k e 4o1(qkwi++ jwbh

Why do we not expect perfect agreejy4z,+b mv +w16xhdrdment between measured values of X-ray line wavelengths and those calculate4r6+bjwzh 1,+m vdxd yd using Bohr theory?

How would you figure out which lines in an X-ray specmfg56- em njw0q)d/m ;jg(vp otrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitioktkgnsi0s 1)/- a-jfkns deep within an atom to produce shorter wavelen igtkkns/0 a1-)jk-fs gths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary c:e0 m 9efcdmec,1e,ht ud 3p2light? How is it the same?

Explain how a 0.0005-W laser beam, photo0kyfp+3rke6tz9c 24u *fjleaprrykm h; -n; :graphed at a distance, can seem much stronger than a 1000-W stree90l6czf*a3r 4pk 2 myejk pr;yheut -k;nf+r:t lamp at the same distance.

  Does the intensity of;gsrw67- n7hqu -crw b light from a laser fall off as the inverse square of the distance? bch;w7u6qw -r grs 7-nExplain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energ 5e(kb :tqjpd,u(2 qqqy $0.40 \, \text{eV}$ 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 withg-7i(1s *d5s(smrsn a+ l z7fk2nqxgt a speed 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 positi c9rst5fp8/eion can be measured 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 an atom f i83mpur+c)pjor 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 mas/5q yi r viua ,qf,fo+v3yhpj 63*zc(ds 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 a neutron conta; ii*glvx9 :vpx1mi-ained in a typical nucleus of rad;ivm1 -ia: x9*xlipgvius $1.0 \times 10^{-15} \, \text{m}$. [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 principle toma)pj vired+:.ijj: 7 show that if an electron were present in the nu j+e .rjp:7mi:ij adv)cleus $(r \approx 10^{-15} \, \text{m})$, 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 oh l o3 g-3wf:g7scp.zjf 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 the s xgy-,(4kn,d1 aqyyqix 1p1h$n=6, l=3$ subshell?    elections

How many different states are possible for an elcejir16 bms/( ectron whose principal quantum number ij rbi1ec/6m( ss $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each )qs/xy az3g2,bpur u .electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground+h0aius d7 nhv: k(o:ytpz 5y0 state of nitrogen $(Z=7)$.

  Suppose a certain hy(/jrp -8v unxgdrogen 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 thef43;t1 ra v/ltln)f r2yl0apv:+dhze 8llu; t angular 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 hf l,h6lh5tk f77nray69.b lmja.n-d q as $m_l=-3$, 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 18fc-jjw5c7 kx*p3x .2 dty *ved electrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for elements wid.e,;j3x yo s9t41lxqhu mwa3th $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electr:7koqi)oxi ,y on configuration for (a) selenium (Se), (b) gold (Au), (c) radiu okq,x :oii)y7m (Ra)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in thekfd hsu66e9f/vb n/ 1q $6s$ 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 thejt19dh- pjmr, Bohr theory. [Hint: Thd1,j pmrjh- 9tis 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 angul2lkjx-0q vn, 7 ys+wtlar momentum is zero for a filled subshell.

  For each of the following atomic transitions, state whether the transitio4dpf6nb2z/2 kz:ychx n is allowed or forbidden, and if forbidden, what rule iskzpy 2xz/6h:2df4b nc 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 i:/ou g92vbaeo n 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 by electrons sti- vy 895+pw)zg, nyid lu)prbriking the face of a) pwgvd+-iy),ni8 zpry9bul 5 $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted 2kjq egyfz yk9w)j9n:1 *qyj, from an X-ray tube have)ykj1z e2y: qg q9 kfj9,*wjny $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengt: d8rn7y ekso*h $\lambda_0$ 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 when a Co (izaw(qr3 m/b6jwzse4x : 8rv $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an 5( s9ozws46uuz,t xhs$n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength f*rj:3glid f(nosp)(3jab z1,o s lz 0jr .gep8or 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 bombarded9 yaj.o- ksz )mao4zn2 with electrons. The wavelensz 4oo2z.nykm a )9a-jgth 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 detached y (ox yb (97xy.t;aaqqued m:4retinas 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 mighx w33xmw mr371i- fkemg47lx zt 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 du)* zq:s* rk r 9uuq07qr6gluafe to diffraction if the beam emerges through qkqsz6qgr *u9ua :frr70 l)u* 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 the He-Ne .n)ywcca8z .h laser?$\lambda $ =    nm

Use the uncertainty principle to estild9meo- 5z+ wvkf9/bs mate the position uncertainty for the electron in the grv95lb m/zwfdk eo-s+ 9ound state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 and 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 small/;vlrg18r by4va ))ja mz*io cest 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 an electron orbit, estimate the average:t+jej l 2nv msc ;d,+fekor44 distance from the nucleus for an 2+t;:fo erjj l4+s k,vmcde4n 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 operatesh.tovi3 o87yfqx3 gas );rr2 z 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 thn98sg,znimp hq):)rv9oq7d:ye , ng: ot fz7o e outermost 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 Moseley pligvi dx8murz g9 uw4ipc sr*n35 t9:*1ot(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 of different 4nx3+z0bcx /xqe n 1nqstates 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 elecv nck:,- vrrnf9e 83wltron states possible for a given value of -rn kv98l,w3nercv f:$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow sliy8obf8 dnhrugu,nql)sdx( l+1gt ,(2 ts in a barrier. The slnn,ud,2fl sxb+)gqhg r(8 dut18 ( oylits are a distance $2.0\times10^{-6}\ \text{m}$ 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 (v lwk 5z2bgv4fr w/w*4 fcmf;model and by quantum mechanics. Compare the results fow rcfmf w4wv2f 5l/gv(b;* 4kzr $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling whh;bwbdv,,r; bf r. f1ith 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 contains a line with a wavelength centered ah ndwjs,l748mt 488 nm. Careful measurements show the line is really spreadn7 4lmh,j8 wsd 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 across 550 V. They are then directer7 a,xr3d3(cdtb(iak d at two slits 0.73ki((x r ,7rcbdtada3 0 mm apart. How far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerate950t ov5ypheq .aj5 gxd across the same voltage. Assuming that the uncertainty in thee59yjp tvoa55gx.hq0 ir position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were 06 la0tqj, gxolimited to the range from 1 to 6, how many elem,j 0la0oqt6x gents would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast wou3js*w j(arg3mr k*hu :ca4a 8bld you be moving if your mass is 75.0 kg? 3j:c* a*4rubrajh8 ga3(wsmk $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 element shows a series of lines with one8mnlzr utf,:ydf5 7/mvj1kw3 out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown element is an ion with Z protons and one electron, determ5zf fum18 ryw 7jl /dn,k:3mvtine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emifia6-t i)j p:ctted from the surface of a certain metal when it is bombarded with hf:aj p)cti-i 6igh 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 l5kw wejt, 7/r1l/gj ucaser beam, $$\theta \approx \lambda/D$$ , 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.]