Compare a matter wavt bh(xod73i. ce $\Psi$ 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 mechantp3fe fnyt(1ttw6 o 77ics, partictpw7t1ftt7(6oe n 3fyularly the uncertainty principle.

Explain why it is that the more massive an object is, the easier it beco * slrue)+0km)th ss6()jm xcames to predict its future urh sa))s +e0x tkjms*c6)(mlposition.

In view of the uncertainty pr01tnixcqz7a( gs5 as ,inciple, why does a baseball seem to have a well-defined position and speed whereas i5a7g(1n s0xcs, qza tan electron does not?

  Would it ever be possible to balance a very sharp needle precisely on its poi4 p9q.a2pe pte0 cnhw5nt? Explain.pq0e2 e4natpch9p5.w

  A cold thermometer is placed in a hot bowl of s9wtv) 9hf efh2k p34huoup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup 94)u fw e h923pfvhhtkbefore the measurement was made? Explain.

  Does the uncertainty prmw(j , yt4tw+j2e2e qzinciple set a limit to how well you can make any single measurement otjm(w wj,z2+eq 4 eyt2f position?

If you knew the position of an object precisely, with no uncertainty, how we w 8hml)gmz*8rll would yo*m z)wg8mh lr8u know its momentum?

  When you check the pressure in a tire, doesn't some air inevitqkf wr* z-;v3hably escape? Is it pkrw v;hz f-q*3ossible to avoid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that mo 1vnt*6b9yin8fn1u the ground-state energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "it 6o19 vfnmn8y nbu*1energy width"). Is this consistent with the uncertainty principle in its energy form? Explain.

Which model of the hydres l,r01*diu0r/k/5 ai iwnwl ogen atom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time near the nl*sr0rl /ii 0un/ w,1ki aw5deucleus?

The size of atoms varies bx29z s/go8g fny only a factor of three or so, from largest to smallest, yet the number of electrons 2fxos n9gz8g/ varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate light as ; o00rzv7uzc(/z sr zothey jump down to z0/szzrz o7(cro u0;v 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 werw/lcjnrf99 k )b6 diyoa(qfm; nxm*9 1e no electron spin but otherwise quantum mechanics werek9 jmyn9rfb6w;om 9ad)ci 1*l/nq (x f valid? Consider the first 20 elements or so.

  Which of the following electron configurations are njb*o zv ca-)2 +wj5azot-5q1l0 pljal. o-hm got 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 (careful scrutiny a*h fp7mdu wqzmec1. 8- dz.6fjcross the periodic tablp76hd mw*ejzf-8qz m1df. cu.e on the inside back cover will provide useful hints).

In what column of the periodic tableamp+jwf -h;gl 1jfc,6 would you expect to find the atom with each of the followi h6-gf, j1fp mc+jwl;ang 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 prope1rq)-f y ;mozvrties?

Explain why potassium and sodium exhibit sim6fbj*r (6s6xmu 4es9sx99m ekrc yht9ilar properties.

The ionization energy for ne(act,st*0 twlv/ e.e. 3mpkjgon $(Z=10)$ is 21.6 eV, and that for sodium $(Z=11)$ is 5.1 eV. Explain the large difference.

Why does the cutoff wavelength in (rja20+u t- bcpec8b* 9w+fq6v -mcesvFig. Below) imply a photon nature for light? 0v-eqac * vb b2 uwrc-+js+f86mc9 ept

Why do we not expectag/m ti7u*7.j: hcvim perfect agreement between measured values of X-ray line wavelengths and those calculatuiaim * 7/h.:mvj c7tged using Bohr theory?

How would you figure out which lines in an X-ray spec,)saz2 8tfrxaqkb5gr(zl 63 ; inu:rctrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitios*i*id; nk c)a u7(h kvpj2/hdp,et 1zns deep within an atom to produce shorter wavelengths than transitions by outer electst2hdv * 1e ;h7cppiu(kida j/k)z*,nrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary lp93 vg37dg oezight? How is it the same?

Explain how a 0.0005-W lasemgdo4ei.gm /0 r beam, photographed at a distance, can seem much stronger than a 1000-W street lamp 4ggme m./0 iodat the same distance.

  Does the intensity of light from a laser fc32xtxg8md 53m qvb ,tall off as the inverse square of the distance? 5q3dvx8 c3xmt 2mbtg,Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic eneryp6i+2pju1fj s f k0y/gy $0.40 \, \text{eV}$ 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 of ot3pr*y op70zwgm/lo wv*32 p $(6.560 \pm 0.012) \times 10^3 \, \text{m/s}$. 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 ca+trn3o4uub,yjo8qlw716 d 8iq-t / c-gewq ukn 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 ofquhzo p/ x tj25++lj1o- q:rkz 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 o/l,v mlr1r7rvc a,zo8f 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 neutronl3w .znw cqi8c9:jjrlj6( lc9a83baf 6pmmb: contained in a typical nucleus of radiu. fr j968l al mnbj ca(wl3:bq :w6c398pzcjmis $1.0 \times 10^{-15} \, \text{m}$. [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 toy*/ uft xs-ew8-yko s9adh6 2m show that if an electron were present in the nucleuxtm6/9o8uw-s y *s-he2afkdy s $(r \approx 10^{-15} \, \text{m})$, 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 pobzmn-+) t ofu(z,jn4u; i2secky0(q r sition 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 crqm.td r7.(rdan be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron n9om zo12:orr b 9k,jwwhose principal quantum numb,owbr1 o2m: 9jznrko 9er is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in thravs3 x8*h0jwe ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground s ;okquf; yf d9k+756 3tjrqnfetate of nitrogen $(Z=7)$.

  Suppose a certain hydrogen a1j3o l/av) z spzkh0a-tom 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 electakkp7z khn ,btr50iv 7cim,)2 ron 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 hn n*fw (k2bfr9 fjx9(gas $m_l=-3$, 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 ar1ox+ q c42p b8.;mmdsz2r ex18 electrons in a "g" subshell.    electrons

What is the full electronl4 cho* /d m9sdpe4z g7w5kll2 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 electr zs 5abzjv8.h3on configuration for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic table inside the bacz3j.h 8avb z5sk cover.]

  A hydrogen atom is im-jyg+wvp87q ;i.lmjm9 qnl1 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 of the third electron in lithiuarab0 0c q+kt5t54 4qll)rbx nm using the Bohr theory. [Hint: This electron 44+ qa b)qt0klbt0r55 nlra xchas $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angular momddhg 6-3 m :d5tap+iqventum is zero for a filled subshell.

  For each of the following atomic transitions, stajc.kgt08ev 77v i) kizte whether the transition is allowed ori8j )0vk.cztk7ievg7 forbidden, 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 irr8 7v6(q qqwon 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-wavel ww7 lpy;fv kig53z51sength X-rays emitted by electrons striking the face of vw ;3zyglf7isk1p55w a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tube have) 2ax)gauf r5p u2xg) aa)fp5r $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff a;6o5gtpmnj 0rz ,0 1o7gkvqjhx4gf 0 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 Co 2.3e1zsolnf80c v xa f$(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength hiivzv+ .e1. hbcb,f1 for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate tqgk(*mzw c82u7srwl ++ko(uqhe 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 j9o fgqdmu ;3.q8uee9q(0nmdbombarded with electrons. The waveleng.qm(quddojg;09 e3qne89 ufm th 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 ,;a2j plswe8 r2gtemb9 3f2/ig;wzzjdetached 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 used in a physics labrq/gengc b: n-xe35 x/uv1g7b 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 eme i*2 rnfaoy*d-rgesy*oi 2r*-a ndf 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 tzv+c0j;xd/yx+u ,wr0 x hzo b(he He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position ullkm6chys287i -i1c+mofi 0encertainty 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 this value and2-l8i kehi c7m oc+0fli s6y1m 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 angulwne-05z ruoa 0:1ztmxar 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 thehhxfyaam -s fj5*+ *zc9)d.nw average distance from the nucleus for an electron in*h xw).n afc+dmj a-*sfzy5h9 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 operatesa,lmr/v q qv+s4 omc92 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 outer)q7m4 b+yzlm vmost 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 plot(Fig. Beloyp/d aejsau/ zraf;ln)sa61 v4 vs.44w) 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 di1uzgwjjmc,juzboq5 t9uc o/x 3 +.o 5.fferent 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 given v1(m j3g 2 jq.xxak4bqqsz3m5 zalue of .jzmx(z1 j 32 qqb35sqgx4amk$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is d+8lgxzb . f:lshot through two narrow slits in a barrier. The slits arefl b8dlxz+: g. 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 gie8bafk9v2pi1jmw85+ ska5 f epbk b/( ven both by the Bohr model and by quantum mechanics. Com2 a+ pepfbj19bs5kw5kma8kiv (8e f/b 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 with a 4lx7;70c7 o+1 xcpi w yojitenspeed 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 containdt*9o(qr xs(e s a line with a wavelength centered at 488 nm. Careful measurements show the line is rx*rsod (t (eq9eally 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 ;ql.fk( x 3qbwV. They are then directed at two slits 0.70 mm apar 3f. qbkx(;qwlt. 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 accele d oker9nz 7 8c*4xsefme;8ou0rated across the same voltage. Assuming that the uncertainty in their p4s zo8;x c*nfm r9e edo0u78keosition is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the w,h0 mow+ psllw0/ dj;range from 1 to 6, how many elements would wmp+w ldo;w0,hs lw/ j0e find in nature?   

  If your de Broglie wavelength were.otx:og z.x tbpj(/*l 0.50 m, how fast would you be moving if your mass is 7ogx/o t . p:.zb(l*jxt5.0 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 o; 0 hemcsp96jcf lines with one 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 eles0; h 6pcmjc9ectron, determine Z and the element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emittea3ex9w8s5badp6 t q jchf 76*md from the surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength corresponds p6e7xbtacjh wf 9a 3ms d685*qto the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread ; *lf4eae.2wm g2lbrxof 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.]