Compare a matter wavrjj4;,w b;odme $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the atom9dh t2wosj lgq13ik t8/6maup9k q *)f is not compatible with quantum mechanics, particulak/ s2tp gq8tiqf 91kouma) 93dlhwj6* rly the uncertainty principle.

Explain why it is that the more massive an object is, the easier it akh(aazza hsjt05. 0. becomes to predict its future posia .0aka z (sha0htjz5.tion.

In view of the uncertainty principle, why does a baseball seem to have a well +lc3fezs i*,t:;pnf -+yf j,z rvh3kf-defined position and speed whereas an electron n3sf:,+ z*yrfci3+fe -zkv; ,lp htjfdoes not?

  Would it ever be possible to balance a very sharp neyr8)f3/ev1 b; sguvnwedle precisely on its point? Explain.1fuw; gr8 b3s v)e/yvn

  A cold thermometer is placed in a hot bowl of soup. Will the temperature read8 +yk 0b7k5pfwfof ;1hu g*rbwing of the thermometer be the same as the temperature of the hot soup before the me0pkb; fg8y51*brho7+k wwf fuasurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make any sin: xtj /jq9ztw*gle measurement of positi9z:t *qw /xjjton?

If you knew the position of an object precisely, with no uncertainty, ho*r6bxsp96z * qt 5cxs:9pacvy w well would yo:qp9p b6ts*r x9az6c * s5vcxyu know its momentum?

  When you check the pressure in a tire, doesn't tm/r:yyzx8:)ba nit0 4duf -dsome air inevitably escape? Is it poss4u8)db:dn xy0 t :-/rifza tymible to avoid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that h 5: uopg+ c*sql4 17dcs/fvnuthe ground-state energy in the hydrogen atom can be precisely known but the excis uln1 /hf cov* s+:gu5pqc4d7ted states have some uncertainty 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 th .d , 1vodq,jbd1*jynke quantum-mechanical model,d b j*1n1, yddoqkj,v. predicts that the electron spends more time near the nucleus?

The size of atoms varies by only a factor of three or so, from large 0/q i,ylxr.fdst to smallest, yet the number of electrons varies from one to ov.r dliq /0xyf,er 100. Explain.

Excited hydrogen and excited helium atoms both radiate light asai-v rzzm4+h 6ehl 9s. they jump down to the l 6h4vrh.z9z eas+-im$n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin bub e13)rzl;e3y qi: flbt otherwise quantum mechanics were valid? Consideree3;)by:bl q l1i3z fr the first 20 elements or so.

  Which of the following electi0 3evmv.m o0pj.k2gnron 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 f8( 3 tk: w s4a6dpk-z.: bqvhowc7tstsor a uranium atom (careful scrutiny across the periodic table on the inside qt t - p73.(8kozvk:s4acbw 6ssdtwh:back cover will provide useful hints).

In what column of the periodic table wodq /a7nfv/4ui8tf/y4:v l pr iuld you expect to find the atom with each of the i lavp7 u/q//:d4ft8 f vn4iryfollowing 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,dxqz++mw dbdmv/c *: properties?

Explain why potassium and sodium exhibit similar propec.w7 e5z h0b gjy4odb.rties.

The ionization energy for neo8d tgh*)mqop l6i: -kh-os ic,n $(Z=10)$ 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. Belo ;v wl5utg4:atw) imply a photon nature for light? tagw ;:5lvtu4

Why do we not expect perfeo 1*0 vmhwrag4xfbpim;m37 6p ct agreement between measured values of X-ray line wavelengths and those calculatedp h*1pmwfvr b64g3mi 7m o;0ax using Bohr theory?

How would you figure out which vnl q8oq7a,he0tyc :. lines in an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom7cjs 0ni 9u6dv to produce shorter wavelengc790 dijv6 unsths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? Hod/6)f0y7kvdl;-il4kogubqc.z f1r z w is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can seem m+c 6tncg) x0xhei7) o5qx4ymouch stronger t m6yo0i)7 x4e+5q xc)nxthg ochan a 1000-W street lamp at the same distance.

  Does the intensity of light from a 27qqatmn;6m glaser fall off as the inverse square of the distq 2m6 7tqamng;ance? Explain. ----待选择----yesno 

  The neutrons in a paralc s *9* ij.fexf 1+-q5cdz+gjwndysx. lel beam, each having kinetic energy $0.40 \, \text{eV}$ 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 speeddm8twjm1r(qco.p/ bt7blm1gv 7w8+ u 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 pos.hvt.rn5:lkb z6arbg hob4 81 ed: ( he0o0zboition 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 atom4) cjmy0 dbz)-ot s0ld 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 wz.8;sal;z2b 8bt3 7q *s8xty1x*zxnt hpsbxin 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 possik-0q qo,xub*gble energy of a neutron contained in a typical nucleus k0o-x uq,gbq *of 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 i+9ay hni .y9luum9q +df an electron were present in the nucy+m9d 9a9unily hu+.qleus $(r \approx 10^{-15} \, \text{m})$, 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 p pk/ c5y91uc5ajqpn w+osition 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 tht4uds(vu l3e4e $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose principal quzv// ,zs:z5 x+iymrtjantum number istzzz y/j/5xr i, :vms+ $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state of kq5d8 cmb4x;i
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numberqc8daarogw-*x/ / sy-s for each electron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom*++o c b,h..krlliimez8 ubt( 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 th7tc otb7-i20p ist;the 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 has og z jbt*j l(zftun 422;h-hf:$m_l=-3$, 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 xilvx z5e+ 90p/0ab rxbe 18 electrons in a "g" subshell.    electrons

What is the full electron configuration3nuy6 gv:y(h z2sxl /o 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 configurati 9urg phm1xx20on for (a) selenium (Se), (b) gold (Au), (c) radium (ph 1rx90gxm2 uRa)? [Hint: see the periodic table inside the back cover.]

  A hydrogen atom is in the sit j0jztj8p,3 i -nn.$6s$ 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 the Bohr th+) odjb;wd cyd1e;g8j1 iv,qx eory. [Hint: This eled,e jvo;) qc18+gxddywi; j b1ctron 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 );ndu,rh je8o for a filled subshell.

  For each of the following atomic transitions, st1f7 lzcaku40l irie4 7ate whether the transition is allowed or forbidden, and7i0 kl447ule 1iza frc 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 in)bbvuffpbp50k rdbuu4)k 10: 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 strik,84w cdpfz/mx ing the face o8xdpzm 4,w/fcf a $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlubnsqv6z3k w r) wt:65xng X-rays emitted from an X-ray tube havez 3n6r ws:kbwx6qt v)5 $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wal6x1trgo8 mwc2 e +mg2velength $\lambda_0$ 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 waveledjny(bq 3mzd9 m:a, iy g-g8k-ngth emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength +d 0wm yyi6e*ffor an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelength bemajk rqed*(;iq:j/ 0d1 f 0efor 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 bombarded with electrons. Thnsr lzy.( 52ioe wavelo52(nylr. sz iength 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 r ;b,x.p9qk5e fpdrm) aetinas 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 might hav dyn. q-5ez9vyqrdo,:e 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 tv7j:a fqg ctj)j 0 /9seogq)+f.pf7bemerges throua0bg7f7/. :jvtpf q) g so)j+ c9tqfejgh 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 He9mn6gz k3uo/i -Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the positn yx/i x 9ijerkyqy3n5bl6w+f ,l89h; ion uncertainty for the electron in the gyyn ,qr3w i98+n xy lhei;j/f 56x9kblround 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 smalles mfio+0vmpy q.ze9xyfz,*8 m(t 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 th-tfd yq)vgs5wp 2n -8j):rxn de average distance from the nucleus for an electron in the iygj) :8n wxv5- 2qd-sndr)t pfnnermost $(n=1)$ 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 rxupbzu1;k5*8 pq-a*jk7p dl $95 \, \text{kV}$ 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 isvyn8mygp,fipumhh 0oj :.* yu6w-n cx* 0*b/r $8.26 \, \text{eV}$.
(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. Below) cah1tvj lm +r8jd mk1; +sdg/t1pmu /*ctn 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( 7tjpwq. qspzya /ehk15rnnw t, a)+0 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 of different electron states possible for a given value ox;qbaysnon+193e* )jbi4 n)ckc zd:v f 1 *s;vbi o)ka n9x3qcd jne4n:zy+)c b$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits in a bat/h*+ji oru8dkwp p .)rriepidu+r*kw 8 /phj t.)or. The 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 52eqo3ti 2( ejigvx*tmodel and byoe3t(2tg5v i2xqj* ei quantum 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 travelini 7 t7+lmb(y8v6 yniqgg 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 wavelength centered at 488 nm. Caxu d4m )ava,s -4n:niwreful measure:dv,m4 xnsu 4na-ia)wments 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 a ayo9vm*a-v(yvz (p.are then directed at two slits 0.70 mm apart. How far apart will the interference peaks be on a screen 28 m apvy(y a.9(v v-amz a*oway? $\Delta y$ =    nm

An electron and a proton, each initb(6hg * gd+: kzlmktje.: +dypially at rest, are accelerated across the same voltage. Assuming that the un+mhpezt k+ 6:j(y.* l:dkgb dgcertainty in their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum nqzfii(v-n++ vumber n were limited to the range from 1 to 6, how many elementsq-fv vi+z(i +n would we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be movb22fxi /k.mpbvfk)c: ing if your mass is 75.0 km): 2b.c2xbkvk i/fpfg? $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 a mboj+lqrf ,v:hj* -/vn unknown element shows a series of lines with one out of every four matching a line from the Lyman series of hydrogf-m,l +:* bqv/vojjhren. 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 from the surface of a certain mfaoi;pe 3m a1t: ab:h8okzo )+etal when it is bombarded with high energy radia1of:zhbt aop: )a oeka8i;m3+tion. 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 be9 rgtkn.- c4llam, $$\theta \approx \lambda/D$$ , 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.]