Compare a matter wav9m+lyd r 4j mfvyfxv 8.vqy7uv9j-(/ he $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theo) (wb;:wbqzmvry of the atom is not compatible with quantum mechanics, particularly the wmqzb v:) ;b(wuncertainty principle.

Explain why it is that the more massive an object is, the easier it b5tq4re5y(0e s1j dednecomes to predict its future position.4ndqsr5 0 ete5yejd 1(

In view of the uncertail;qbp.0.d tqbfhq7s0 nty principle, why does a baseball seem to have a well-defined position and speed whe0flqd bsp.7 b.;htqq0reas an electron does not?

  Would it ever be possible to ba6fcmpj6w bx5*r28ugo lance a very sharp needle precisely on its point? Exw5*pm cg66f2rujb 8xo plain.

  A cold thermometer is placed in a hot bowl of soup. W,xld*3 ktmctj)8:epf* m p-f vill the temperature reading of the thermometer be the same as the8)*tj m*m d3fk-cxl,et pp:vf temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how welf8fj upih7o8cfu.:t6p:btq ,7x3 mm gl you can make any single measp: 3 ugxfm8pfj,u 7t b.h7cfo:t8 m6iqurement of position?

If you knew the position of an object pk b6ktlc en5w9 1g)df kj47k0hrecisely, with no uncertainty, how well wobk65jkfg0e) whk1ck tl4n79duld you know its momentum?

  When you check the pressure in a t s +8xh9qqqzej.-.j8t hae qm*ire, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to ttq.jsh+ xzmqehq 8.- q8e9ja*he uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom*ty : 8zsbym+p 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 for y8p:mb+t zys*m? Explain.

Which model of the hydrogen atom, the Bohr model or the quantum-mechanical mode5fca+nzb.pa r 58/ wial, pred8aw/5b+ncrf. i5pazaicts that the electron spends more time near the nucleus?

The size of atoms varies by only a factor of thrk gls vj2ifb d(;8(a+nee or so, from largest to smallest, yet the number s 2 fv+j8alngkbdi(;( of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jump do(rnu fd0mqegt 2:ki 33wn tom( tnqd32:gfr3ike0u 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 ts+)qm i+w5g jlhere were no electron spin but otherwise quantum mechanics were valid? Consider the first 20 emg j+5isl qw+)lements or so.

  Which of the following elhvhqo(r ww ,-/-6q/1 jduj neyj*t/nqectron 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 ur -p rc:h/(sdmbwbfm;e67d k wi2 da/9ranium atom (careful scrutiny across the periodic table on the insibwik7:;d we 2dh 6/mc/-a(mfs 9rpbdrde back cover will provide useful hints).

In what column of the periodic table would you expect to find th7al d 2yrd.k8ke atom with each of the following ck.lr 7adk 82dyonfigurations:
(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 iode *0;rw u5r iq5;3ivzpd wkza5,m5jbnine exhibit similar properties?

Explain why potassium and sodium exhibit similar propertied.osyx d(p5buq o/ 2s)kc +*pus.

The ionization energy for neonb/8yd+ t7dw hx $(Z=10)$ 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 for lig;(33f,rp ug 5fiokbscht? (u bf i5;pkf3,scr 3og

Why do we not expect perfect agreement betw)0 itft26zwfx een measured values of X-ray line wavelengths andz 2it wtff06)x those calculated using Bohr theory?

How would you figure out which lines d f.g18h bmfegncz302 in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transe7uyw3/ ivjuky /u/y6itions deep within an atom to produce shorter wavelengths than transitions by outer elku y/7i u/3ejwv6yyu/ectrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How i70sd sv q/yz6ys it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can qc-f1h f fz2wbv8 h)y1seem much stronger 1vf8zqwchb 1 )ff-2y hthan a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as the inverse squareg60 yh) ecmus2t ;8ojm of the di;8t0ju gm26yeso )hmcstance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energy r+ r8eha l.-hd-svf3v $0.40 \, \text{eV}$ 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 s(ewdf o 2ab.ik3uw 3p.:k4a0b/ 2jx8 yxts juepeed 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 measured tok60+ r mhy;j(irn as)s 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*unlnk0s f*w:.ysb(r of 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 in the mass of x,m0,z1ox +pi0:fy3 3npiaf ib x2nan 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 possn9d+h fdbm/:t ible energy of a neutron contained in a typical nucleus of r/f 9bdn+hmd:tadius $1.0 \times 10^{-15} \, \text{m}$. [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 to show that icpmpl8w8 e40. h1maxef an electron were present in the nuclw8lex p1.ecm4 amhp0 8eus $(r \approx 10^{-15} \, \text{m})$, 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 pwo(dg*7xmev1d s5b deev-: . position 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 ( rf/ c0tv 6guuov)a,obe in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose princ31 o;fxp w/xiino6h 8cm1 mr 34ijgno(ipal quantum nujhm43i/6g xowr (nx nooi1pi ;8m3 cf1mber is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the grounoji47td k4 4iud state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground state of nitr):c y2gcz)8h.dm ipg ybx0. mpogen $(Z=7)$.

  Suppose a certain hyrbo3 5np8a z*e(n p:xddrogen 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 mome ig-itxlun. cbfjaw1k0e9o3h 6 58 k/nntum 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 hx(vw yc 4;mmet9fso 9q6:tot8as $m_l=-3$, 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" su yrgy.7dzd2p0 f w cp(yix,i4uu:-xx:bshell.    electrons

What is the full electrljs0o *ouet +(dlx+v -on configuration 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 (ado2/y4gx 1yoe ) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic tableyoy4/ox2d1 eg inside the back cover.]

  A hydrogen atom is inv6/uub2u6)g/ zyxj nl 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 usizq8x vvbb6x ub7j3** ong the Bohr theory.jz*bbbxxu*v v q 863o7 [Hint: This 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)o twx0bqw)y 6 for a filled subshell.

  For each of the following atoz4r49m,h.)kz- sgosw zcho *ymic transitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is being violated: kzowz*rhg,4hmscsz)94. o - y
(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 r8ko0 svpj-5d 9d +skxhg2y(hin 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-wave/ h fvlv6uk4r;,q *oqilength X-rays emitted by electrons striking the face ofvkohfq/ 6v, u;lr* 4iq a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-waveleo v038kx e4lmlngth bremsstrahlung X-rays emitted from an X-ray tube haveo0vlmexl38k4 $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelen f c mn*bunt(0-hrm).f(phdv eyj g+)zj2i9j-gth $\lambda_0$ 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 wavelengt4t w9ln. it3a*bvi /r)gx3jvmh emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelengthyzyz ig( yopw686y.b; for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength for an w2 p5ui5c,hwy$n=3$ 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 bombarded with electrons. Theubpug37.n8a n wavelengunb3gu .pa7n8th 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 retinas pux+nc n- :5(pl(kgx 7r5ilbwvu ts 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 mwkz8to0s8z8physics 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 spz d,q37avl. vsread of a laser beam due to diffraction if the beam emerges vld7z,3v. qsathrough 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 thertp, 5+hxeuqw:1d.cg He-Ne laser?$\lambda $ =    nm

Use the uncertainty princrxlzdi) 08. x6oet x*jiple to estimate the position 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 assume the momentum can be anywhere between lx08 ) dj6oe*rz.ixtxthis 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 for the 80 5nqri-u ;kufuq(vfk jh3j. 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, eqhb( ne)1yr1-pke( *y:ykx2yua9l z4 alvg t+stimate the average distancqynrl(g p2et*y4z1yk(e-hv la1kaxu :y +b)9e from the nucleus 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 operates at:iywp)jbq+/t $95 \, \text{kV}$ 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 ele2tpw u0/xz )8vj5 eiwhctron 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(F0:bgq0g ) gr7lvdy nxs2v0 w+ebn4f*cig. 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 diffel,9; *2y :osvq uwufmzrent 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 states possible for a givent 7dv tgd yt69c5g nb8y/74rgh value of dd5 tgy4tb86thvnrcy7 gg / 97$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with eq7l hpgb ajks3g 05,i6:x+ldp nergy 45 kV is shot through two narrow slits in a barrier. The 5:3,sjdkh6q lgpal0xg p 7+bi slits 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 model andq +ipenm6bh 1: by quantup h:+n ei16qbmm mechanics. Compare the results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling wite08coe 7*8zfl*yj t 4x9abijyatg)( jh 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 cent o)1u cx57evkxered at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate th)xx5c7 uovk1ee lifetime of the excited state that produced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest across 550 V. ow9n mclznn4+z l(w7e13 mt(lThey are then directed at two slits 0.70 mm apart. How far (e zo3l+(mnlc14nt 7 9lnwmwzapart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially n:/fg/4xldeymq7 tw - at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainwf -qdly x 7g/e4t:m/nty in their momentum.

  If the principal quantum number n were limitedq2 c -qn17rceovk d(f( to the range from 1 to 6, how many elements would we find inn((er qqdc1-kc72 ovf nature?   

  If your de Broglie wavelength were 0.50 m, how fast wogn :j*nfhdszx8acom 83 a,1j9uld you be moving if your mass is 75.0 kg? s8 aj*:93 nnao, d1cmj8xf hgz$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 w7gha* 2 zqx qic2vp+ 2d7pwbm.ith one out of every four matching a line from the 7 za7q gpq dhc22xmw2.b+*vpi Lyman series of hydrogen. 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 fromgg)cn gm ;b kzm(i5 c.6+x7sgi the surface of a certain metal when it is bombarded with high energy radiation. If this phocgbmgc g;)5iz.6m ng k(+s 7ixton wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffracti5,txlgrfu(a; ve spread of a laser 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.]