Compare a matter waveuoao1 0j2mu,(q4r *kaxuige ; $\Psi$ 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 compatible2 *p8hek.a8z b 65vjhzx6qwbx with quantum mechanics, particularly the8zzkx 2h* ap6.86qwb5bxh evj uncertainty principle.

Explain why it is that the more massive an object .iy lv 6s-lva8ei-; yfis, the easier it becomes to predict its future posil vye--6i8vayf;. ls ition.

In view of the uncertainty principle, why does 1a rwmweg39 :wa baseball seem to have a well-defined position and speed whereas an electron d9aewgrw:31 m woes not?

  Would it ever be possible to balance a very sharpa,s/d 5mjp ay:v/xkm3 needle precisely on its point? Esdm5v jm:/ k/,x3 aaypxplain.

  A cold thermometer is placed in a hot bowl of soup. 9j 6fekwyx0w )3x3tybWill the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement was made? Exp 33yftxx)w0 kjw 9e6yblain.

  Does the uncertainty principle set a limf8vnoe-6s u:pit to how well you can make any single mp6eunfo - :8sveasurement of position?

If you knew the position of an object preciselyz,z yy)0zkgdfby 0d 9s, v*s4f, with no uncertainty, how well would you know its momentumy4fz* ) yvzd9gz ,0s0dksbf,y?

  When you check the pressure in a tire, doesn't some air inevitably escape? ;wny;j6n8w qlIs it possible to avoid this escawn6;;n wl8jy qpe of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-state energy in the hydriln9keh5/i qtgg8a- . ogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertag l5tk/ gie -n9qa8h.iinty principle in its energy form? Explain.

Which model of the hydtd; en osi*2avs )s+/xrogen atom, the Bohr model or the quantum-mechanical model, predicts that the electron spe e+ 2x*dtisan/); sovsnds more time near the nucleus?

The size of atoms varies by only a fact pxl fnieog,uv80*-vsy 2l6u-or of three or so, from largest to smallest, yet the number of elect-iu,6xvy g* e0ll 8- 2pnfousvrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both radiate li/ptpyw::1df 53 wk bepght as they jump down to thep1f3e: dwb /: twykp5p $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin butg160) higolt*qh cnx;qae zm.:kgz:7 otherwise quantum mechanics were valid? Consider the first 20 e :o61zlgin ct;.ghaq*q)h0eg:m z 7xklements or so.

  Which of the following electron configurations are not ali,z1xvt vqecn y39z q* 0uc5r(lowed:
(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 u-9 +e8allyqjf ranium atom (careful scrutiny across the periodic table on the ins9+ ly -8aelqfjide back cover will provide useful hints).

In what column of the periodic table would you expect to wykvfqm*1ap iy 6ljbtn95/3;find the atom with each of the fo*pn k6/qjb3li;tyf 5 wa9y vm1llowing 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 iodin+ga l- i od/.lxxzn(o1e exhibit similar properties?

Explain why potassium and sodium exhibit similars-7wl z*vn1i;fjj zovzj8 lo11w,3jqm7br +z properties.

The ionization energ4jfmraq ;rzoq2zu-8 )y for 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 wavelengt3c01 fm+q/jsp q+hr kugp* of:h in (Fig. Below) imply a photon nature for light? m p 1uprgs* 0fjq+o:h+f3qk c/

Why do we not expect perfect agreement between mt)+ ra uvxc*p.ahga00x )r x5neasured values of X-ray line wavelen))cp .xugataa 50hx rxv0n+*r gths and those calculated using Bohr theory?

How would you figure out which l n3)cw q: 5ibr4fiu3deines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within bk(obfm/7 z3o an atom to produce shorter wavelengths than transitions by outer z3b( oo7/bfm kelectrons?

Compare spontaneous emission to stimulated emission.

How does laser light diffn wr a6quvtv:) nu6d)0er from ordinary light? How is it the same?

Explain how a 0.00051 dtoog;l//oz j)xzt2amh* i. -W laser beam, photographed at a distance, can seem much stronger than a 1000-W street lamp at thxz;t*2 l1/m jd.)/o oti hzgoae same distance.

  Does the intensity of light from a laser fbl.lm/p +a b0tall off as the inverse square of the distance? t/ba+blp .0mlExplain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energy jod .ham:,mh,s.;)fci3.nnlzjvm z u04 a8xd$0.40 \, \text{eV}$ 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 wit zlajquxc/1,e wm-(9bh 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 c5o;pax v- bw(lan 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 c7n*f- -falq qan excited state 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 s;ql5xpvegs 7iqd h 484;7cdia 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 contx+rn:ma9i2m wo rh85ag*rs4 bained in a typical nucleus of rb9*a 5 2xis4:8mownrh+mgar radius $1.0 \times 10^{-15} \, \text{m}$. [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 if an electron zuel((8 7m pekwere present in the nucleu(ee(u 7mk8z pls $(r \approx 10^{-15} \, \text{m})$, 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 s,q3wk,u9gpip+8 p :oz fke n8a $3.00$-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 c-bt)y - bnx,zyan be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron hpt6/z9nwdz- whose principal quantum numbehn9 d/w6pzz t-r is $n=4$? Write down the quantum numbers for each state.

List the quantum numbers fo vg0;;x+pcoiz c7zz j7r each electron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron - v6(h gco8yzrdn p,+hin the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen 1p3,* .zcwyg:v tvvz vatom 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 electr fgga :gd;7* 2/pbiuhton 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 hak 95/yjx5qmc sf ik3r3s $m_l=-3$, 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 electqyu*7( 4aq wjjrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for eleme/zh qiz7pwuhg787f 9pz b*b.osvl26xnts with $Z$ equal to (a) 27, (b) 36, (c) 38? [Hint: see the periodic table inside the back cover.]

What is the full electron configuraty(wos,xw5u0p-: :fu:jz d y+/**e lnwhjir uvion for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: see the periodic inxol s rzwuud:y+:jey( 0*:5j*ufww/ v -p,h table inside the back cover.]

  A hydrogen atom is i7q usl+p08q wjn 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 thirdo k v4haq18 nsz7r.e d5gune5, electron in lithium using the Bohr theory1,ok.r4auqh57ze 8n gn dv5es. [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 zerot );-fn(zdfi8xqt4c5h xrw u; for a filled subshell.

  For each of the following atomic transitions, state whether the trarobu ) i0 xqln5v 56qyu+1hrz6nsition is allowed or forbidden, and if forbidden, what5rqy )bl6uo zuv 0iqn6x15r+h 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 isyk8 muqks);+r in 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 strikinw(dybv7fq;w3 h79*h x 6 wsgtfg the face of t9h6*h wdg3s(f v;xfw yw7q b7a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from an X-ray tus tra7jp. 8.bmbe have a p8.b7trm js.$\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengtx s); i8.0hfqbr1vnvxr5hwv*(2o q cih $\lambda_0$ 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 wav(n-dpg w- bhu8elength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength ftrswvdgt a,1 9od *j:+or an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to esti wxlllp e w-0y4z.wq/,mate 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 is bomenspsu :ihb3, 6cx*l-barded with electrons. The wavelength of sx* bhce us:3pi6-n,lthe $K_\alpha$ 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 retinp 1,x ovd3dh2aas 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 mw)c*xc1 c/i;t s *qscenpj6 yty47xl5ight 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 srx5yf. g0 p vv-rei1y66c j7appread of a laser beam due to diffraction if the beam emerges through a 0r ypcpy651i.7j age rxf6v v-$3.0$-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 lo8s3e x+zb2x 1b)le-qz-cu j jaser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty for the elg;/8e7)f y( e)d s sbcjfofl6iectron 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 and zero.] How fs go) s)86fljiefbd (/yce7 ;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 th/ i143nai rlpie 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, estimat9bdy -bz;0llf e the average distance fro0;-df yzbb l9lm 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 operatep5yb0shd7 2n ls 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 outermost electron in boron is b)vdork4yr+t5 02mza5jr-cxi7 b6 eo$8.26 \, \text{eV}$.
(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)qtsn 8be 2n0fxt ;mo 6(jh(by 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 number of different states for aw7ze 2wgd3l)c6u8yos uts ;j 6 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 valuezh+e)boyre4q 94b;jt of rj9e;bq zh)4o by+4te$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons rtpuvjl8d;2-r8 f xm 1with energy 45 kV is shot through two narrow slits in a barrier. 8xvm;r8-r2td pl1 ujfThe 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 botw3z;/fm t;t-p)yqr- iv7qvbc h by the Bohr model and by quantum mechanics. Compare the tfvcmy-bq - 7zv/);i3;wptrq results for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is travels oi/ 1jqxg91*c osj1ping 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 a line with a wavel4 j:bio 3k; r8hv7qymb.wj(xz ength centered at 488 nm. Careful measurementsoj3;(bjixrh7vz wybm :4q8 k. 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 the z9+ q d5,; nd9k;pidjuzf8swan directed at two slits 0.70 mm apart. Hos uj ,kp9; dain;+w8fdz9dq5 zw far apart will the interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially;ywqcokg 6on20, ) yr f4dwse- at rest, are accelerated across the same voltage. Assuming that the uncertainty in their posi ,okqe0ng 2w4 6yfso)cy;rd w-tion 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 range from 1 to 0 oewzt j;* ;h0mf,qdh6, how many elemen0df*oh z;e thm ;0,wqjts would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if youphngq 5, wi7bzre2 2,5zyszt4 r ma7r, z25e qzgnizwyspb t,4 52hss 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 shq+ ;x qn4v5olo9(6yxyy s1lkoows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the un+xq xoly(nqy61 5vo9o4 ;slk yknown 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 surface ;ljxkr ;.8pxa ti g8/ kndv0/c:kem/pof a certain metal when it is bombarded with high energje:8r;. 8vcnkkd/a0px/ / gl p xt;mkiy 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 bej8;s3/xvwt m5:e3hpffv lh4 bam, $$\theta \approx \lambda/D$$ , 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.]