Compare a matter wave5;xelh zo8e -g $\Psi$ 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 compatible with quantum mechanicssd2, d ygqb7l(, particularly the uncertainty pri(qlgdd7 ,ys 2bnciple.

Explain why it is that tbk) /ax- 1dwqlhe more massive an object is, the easier it becomes to predict itsq/d-)k1l w xba future position.

In view of the uncertainty principle, why does a bas 1r*x* spp1i d+mzgm(reball seem to have a well-defined position and speez1* mmsd i x*r(+1pgprd whereas an electron does not?

  Would it ever be possible to balance a yawqc6b :*ys/ very sharp needle precisely on its point? Eb:cy/ sqawy6* xplain.

  A cold thermometer is placed in a y4x gpwt zj3m(hn,)/gwqh:2q hot bowl of soup. Will the temperature reading of the thermometer be the same as thepmg43hqw2/wx hg (tz)yn:qj, temperature of the hot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit tonz cc.yqr:u;x qylhd 4-9oc:0qu 4b7 rso(wh0 how well you can make any single measure0lyc cq9wy ouqhq :h40z.ncb- r4x7(srou: ;d ment of position?

If you knew the position of an object precibjh,q yo)- lfki,ca16sely, with no uncertainty, how well would you know lj6 ak 1fcq,y ,-h)iobits momentum?

  When you check the pressure in a tire, doesn't some air inevitsu1 1)6w2nx slydk)xlh( evh*ably escape? Is it possible to avehux *sxv16wnl)l2sy1h k )d(oid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydrogen atom can be preb4rh.php/ a4 z43kl ewcisely known but the excited states have some unc brh4z pe4k34p/wh.alertainty in their 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 the2y6tj;o r+aa7:ewzqd w1d 51uugm l 7l quantum-mechanical model, predicts that the electron spends more time near thlwt 6;urje15:+odd7a7m1 2 luwz yagqe nucleus?

The size of atoms varies by ;sajb b,*dpo. only a factor of three or so, from largest to smallest, yet the number of electrons varoa*;bbjsd .p,ies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as they jumpa i1ke8u34ftr down t1irfkae 8 4t3uo 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 nd;)g.d r5n im7otg -nmo electron spin but otherwise quantum mechani gnm)ndm.ri;t -o5d 7gcs were valid? Consider the first 20 elements or so.

  Which of the following electron configurations ao+ rie9vn(rlt s3 c/:cre 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 electroqe q);dbm r48dx u*z 5uz4xu9en configuration for a uranium atom (careful scrutiny across the periodic table on the inside d xm89uzudu*b5e; 4x)e4qqz r back cover will provide useful hints).

In what column of the periodic tabaa ;taa7w/l3rs.7 pzcle would you expect to find the atom with each of the following configuza 7./lw7araapt;c s3rations:
(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 propertied )wpeb /keh. .ro7w-cs?

Explain why potassium and sodium exhibit s.jlrypdot5*aua3d (ks 0 /6 qsimilar properties.

The ionization energy fog zh b (j:9lluafcp9 50pgf*3yr neon $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff +yop-q5tmg q md(op:5wavelength in (Fig. Below) imply a photon nature for light? +- 5go:ptpd( mo5myqq

Why do we not expect perfect r j 0zw jb8-3;98mbepf3geuqn agreement between measured values of X-ray line wavelengthrj8wbuz9j0fb ;q8 3 pe-ge mn3s and those calculated using Bohr theory?

How would you figure out which lines in an X-rayuyaey9,j/jd 8mkt/ h/ spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to produce shorter wav4pnyi o 9vzl evu*o)-4elengths than transitions by outer electrons iv*o9v-ol )pnue4zy 4?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? How is it the samphw0s 4,0j5 6gxf1zwtjho z-ye?

Explain how a 0.0005-W laser beaml t; qgv vy-wr36wzp42, photographed at a distance, can seem much stronger than a 1000-W street lamp at the same dirw 26 34ywv;p zq-vtlgstance.

  Does the intensity of light from a las xa i bgn1(q2-hvwn 77cgyqc5+er fall off as the inverse square of the distance? Expl 71i+gqnn2 7 (chvbxag y-5qwcain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energpm7ffpo ;sxu-vu0 +7cy $0.40 \, \text{eV}$ 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 wi lq hw* 0o3527-z;h2x.sza vtpzyufaoy6 zi*nth 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 position can be measured to an accuracywgcna9-5fq nt0lus1n0(-d d y 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 for f/ y ;t:decod;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 ;:i9gajj -ck s*uh v.ein 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 of a neutron contained in a typicaalncup3 3,u smf3**(5mpwlsy l nucleus of radia*lw(fcmu, 35* n3pusm lpy3s us $1.0 \times 10^{-15} \, \text{m}$. [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 principlehy t3n: xp-7bo to show that if an electron were present in the nucleush:bp 7xyt3 o-n $(r \approx 10^{-15} \, \text{m})$, 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 posis umx2 -n vrl+9,5cyz/ hot7aftion 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 thmv2m 3s4ok/xce $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal quantum dvv hrk(g )h1p1m,zork p22et 5 v1t5znumberdo21vt(h2 hvz5 m ep,rtg1 zk vr)15kp is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each edxt +g 36khkibh+ t*-ah/qwr: lectron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each d4ukzw9nn1lq8y6 i y) electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hyco9a((v (bf;.qbovb 1dp2 mpcdrogen 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 momentum of an r g: kn,lxr4-sclwk zop ,q8;5electron 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 hasp8sgi8 v +qzp. 4cmn2f $m_l=-3$, 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" subs nkncvdh7f*l+(m ap9 (hell.    electrons

What is the full electro4eir5 rxeg h )cfgl;/9n 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 (a) seleniumla av68csp:c6yi t19.skaw 8u (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic table inside the backvwaai 8 l91ct 6a6k: .sc8suyp cover.]

  A hydrogen atom is its um5pm04nm0j n2-ibpp k3.u n 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 o 0( sadhs3s cu;nw8po)*o*ku mf the third electron in lithium using the Bohr theory. [Hint: This electr* *s)oh nsso( 8;au pcuk30dmwon 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 mom. hrkioqa3l*9f * ;ufvj+aj7centum is zero for a filled subshell.

  For each of the following atomic transitions, state wei+.)h ar.u geesz6 :rhether the transition is allowed or forbidden, and if forbidden, what rule is being violated:ri. ge)a re u6hse+z.:
(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 in ayw ra;i),*etm jemac1o yl496 $6d$ 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 strikingvdts+9 3pwlvqzv.9c6 the face ozv3d.pv9vqcw9 s +6lt f a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bre8n7n.33sx )teuehi ohmsstrahlung X-rays emitted from an X-ray tube havee7 )s8.ux3hhnt 3 ioen $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff + 9tsx/xgnlp4 wavelength $\lambda_0$ 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 ebjyqy; o2nj,3ib(tw,1ypf6 Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for*0 :8fwr )xoqiiq*efpoi xi *ge/ew1 98.xflq an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estima-w/qm4sl1 7.mo zjfr2 avo) vcte 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 and an unknown material iss3tym9e+z 0pc1zhg1b bombarded with electrons. The wavelength1t h mzgb9p0 +zs3yce1 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 ret.bzj2n6opmo .xcydk7a kb5 /2 inas 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 mxwe,1g, px k +7cs2* g yf(ctc*pxv7da 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 diffraction if the beam emergo9 oy pgbl;o62es through 9 opoy6l go2b;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 t;xn5oa y)eh8okb88vuhe He-Ne laser?$\lambda $ =    nm

Use the uncertainty iacd .e :z, nl)n(;xrpprinciple to estimate the position uncertainty for the electron in the ground state of the hydrogen nl;ai (rc xpze nd.:,)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 smallest possible values for the anz 8h cnemdcvajjr.u9k89h846 gular 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, e23:u 2voxedaamnk; p2d9ch) qstimate the average distance from t:)d ;32 adnhuoem2xcpv2 ka 9qhe 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 ato cgw e83js11c $95 \, \text{kV}$ 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 elfof fsu bdv.a(tw)5 pil8lm:-9ukc:+byu( s;ectron 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 t/99u x4de ;a3omaytpbo show that the Moseley 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 numbe0ox2 xj.*t0e;;y4caynvjm q wr of 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 ofyd:.v jt 5x0 :8qoaxzx different electron states possible for a given value of xtdz :5ax.oqj0:v 8xy $n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV isb)) .ln,5 .p+vth ahhjn.)x3i lphqcv shot through two narrow slits in a barrier. The slits ,nvl 5hh) 3vbpx.j)i+hca.p. )qn lht 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 i4fuw:qn x i yx 66a-zs9-ed)fhydrogen atom is given both by the Bohr model and by quantuxw)q dfenx: - -yui6a i649fzsm 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 trbzo:-t +1gc; hq/ob(rc 8 3imghkt/ncaveling with 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 y:593olzwxgb5 tcba - a line with a wavelength centered at 488 nm. Careful meaxla5zy9:b-g 5b3wco t surements 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 across 550 V. They are thend t(pu;mlbvhy+c8() .u +yy do directed at two slits 0.70 mm apart. How far apart will the interfe lh mucy(+yu+d(tb)o8 d.;vpy rence peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelkud -ubol pfy13*p kid)+;w.p erated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, fi.d1u +;-)kwfo pb *klyi3ppudnd the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the lo2d g( 8flut2range from 1 to 6, how many elements would we find in natuol8d2g lt2fu( re?   

  If your de Broglie wavelength were 0 )2qjlft iq65p.50 m, how fast would you be moving if your mas6q 5tipl j2qf)s 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 element shows a series of lines wi +f-1rwllcz1 /fxk+ rwth one out of every four matching a line from the Lyman series of hydrogen. Assuming that 1l+rfw-1l+xwfzkcr/ 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 emnuv7r::sh x(oitted from the surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corrers7ux h:n ov:(sponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffrac8 n m0yid d8ncl+3t8grtive 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.]