Compare a matter wave;8 om3dwa: fck0mclk 7wk5q(j $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's theory of the atomx;q n h-ylsb zm8 (7br00xil:/wgzvr: is not compatible with quantum mechanics, p0lx8/ n:-mr hqsbzrz(;7 yi g0bl wx:varticularly the uncertainty principle.

Explain why it is that the more massive an object:s5cp) 7gj,vbc- hgg w is, the easier it becomes to predict its future p,gsg 75gh: )vj cb-cwposition.

In view of the uncertbwb yfut,zjm9l1-sy c*1 i 1soy8v8/h ainty principle, why does a baseball seem to have a well-defined position and speed whereas an electron does 1i9wshbyucjl o* f-8b1zy t 8,sv/m y1not?

  Would it ever be possible to balance a very sharp nevvynva.j* 6kav,) uomw5ix*03co4ubedle precisely on its point? Explainou 0mvb *nvij)ky4 w.v, coa36ax *u5v.

  A cold thermometer is placed in a hot bowl of soup. Will the temp-)atod/rea/+y8j 1-a hrl ocm i5w h6kerature reading of the thermometer be the same as the temperature of the hieo-/ aal-jho8kh 5+ wmy) ar1trd/c6ot soup before the measurement was made? Explain.

  Does the uncertainty principle set a limit to how well you can make any single m q (uy2hoadhwa 7f/yu1 60cj0eeasurement h /0a602jd(feacyuqwo1hy7 uof position?

If you knew the position of an object precisely, wio r4;i//olcdfk+iq 2jth no uncertainty, how well would you know its mom4k;2i/fj oq +dcloi/ rentum?

  When you check the pressure ipn94hvh( 9wk4: m;zp .aub sytevs3.hn a tire, doesn't some air inevitably escape? Is it possible to avoid hb 9:st.evk3n9 sz.4u p(hwa;mh4y vp 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 precisdsi yqshuesci(.3j pt i;4+13 ely known but the excited states have some uncertainty in their values (an "energy width"). Is this consisten3ec j ;yh.s4(3pisisi t+uq1dt with the uncertainty principle in its energy form? Explain.

Which model of the hydrogen atom, the Bohr w*e(ucm t7,3gnexg.k model or the quantum-mechanical model, predicts that the elect u3n*xg7. kgmw(e,ce tron spends more time near the nucleus?

The size of atoms varies by only a factor qvm362zo / veyof three or so, from largest to smallest, yet the numb/6 2zqmo3vveyer of electrons varies from one to over 100. Explain.

Excited hydrogen and excited helium atoms both rad1ncb i1*jd 5ojiate light as they jump down tco5 1*1bdinjj o 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 no electron spin but otherwise q os4 *l;cyrc peh8 l);vqzlm1;rxr50ouantum m8yz pl0qrv esch41 l 5xc;)o *ro;l;rmechanics were valid? Consider the first 20 elements or so.

  Which of the following electron configurations are not a- 8fplp-m8nim llowed:
(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 scr2yzou2v/o0or lk 1(kautiny acrosslvy zr1 22uk/(aoo0ko the periodic table on the inside back cover will provide useful hints).

In what column of the periodic table would you expect to find the atomqtmr;s6*b7kut wk /x. with each q tx;6 rt/mks7k *.buwof the following 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 similab mg (rvm m1zya;50c6fr properties?

Explain why potassium and sodium exhibit similar propertie59ia yl*s spuqdrit pd 14i(n93. imv*s.

The ionization energy for 5y +81jxn5j(jg 8 y rlulikx4mneon $(Z=10)$ 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 light? srlfh5rh9h + w8kr :)y5hrr)hr ys hw9f kl8:+

Why do we not expect perfect agreement between measured values of X-ray line watl(8vzg xxdh .i71 d w-iwo*;lvelengths and those calculated using Bohrii7d lv 1 lx;(8x*gdtzowh-w. theory?

How would you figure out which lines m6iq 2wz *r;+a9k gabjin an X-ray spectrum correspond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to produce shorter fllx+2aty6ls q: -coab r1v2 9wavellbs:o1 cl ry+2v6t2-q9xl faaengths than transitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light d;;-doyr .dy+ tmac3msiffer from ordinary light? How is it the same?

Explain how a 0.0005-W laser beam, photographed at a dd30x6ik fw,yq91o g5 ayfatcb6 ko9-wistance, can seem much stronger than a 1000-W street lamp at the sa fq5ya9- 3 6fw1bgkd6ox0a ctkiy9ow,me distance.

  Does the intensity of light from a laser fall off as thej, gk5e v4mub/8loi c8 inverse square of the distan ,ck4oeimulvb/j g 588ce? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having 6l- nskatq /w.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 w9(7e is;uzw6jmklm/+n-g z twith 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 positionk b1;8onx dztpt) jw l-f7nh,z3s4cn2 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 atom for typirl, q* m89ibgically $10^{-8} \, \text{s}$. 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 a(xdixi;vll f 5 :x/1zl 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 neutro867*h 1n wdi1ak jdhtpn contained in a typical nucleus owk hnjptd81 ia67*hd1f 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 were present in thi phrw0b62 ghia* gf *pvg;5w4e nucleusrw2*hp5*piig b6f4 gg;v 0wha $(r \approx 10^{-15} \, \text{m})$, 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 positb0llb:+r/eqr dwevc61h q0vg t7+pw8 ion 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 txshe +d-7 ppu)he $n=6, l=3$ subshell?    elections

How many different statese bg2pe)o2 ecclu5y+s5 234, heazj eu are possible for an electron whose principal quantum number is ugs55jc eep2 )b yz422 hu ec,3elae+o$n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electbu8 3 m:xysbp9rmk/ 8mron in the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electyuxgpt9:h 8u6v4tt8g ron in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen ato55k:tsh ekl137ta63zy 2lem /cctzkj+ q dep, m 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,pjywlo( h* cl5k6t; ontum 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 jpv( d 000nf)h-whmn7k+w nh/s-dezx$m_l=-3$, 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" oq1nne;xfed; f tt3mi 1d(;3g dc+tv*subshell.    electrons

What is the full electron configm3)gjx80o) xix k: mhouration 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 conf jg3-b twf7x-viguration for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: swf v-j3tx7b -gee the periodic table inside the back cover.]

  A hydrogen atom is in pua x.lwjwuo.x/. g( :kmeo8: 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 jhh9oi o 2g76eof the third electron in lithium using the Bohr theory. [Hint: This electroi9 2e6ohj gh7on has $n=2$ and "sees" a net charge of approximately $+1e$.] The measured value is $5.36 \, \text{eV}$.    eV

Show that the total angularo866 6ev:sovgyd 0 oau momentum is zero for a filled subshell.

  For each of the following atomic transitions, state whether the transitiom phg0+ iqu. afc,tbfic- c2(/n is allowed or forbidden, and if forb q(u0t2+ m a- fcg/c.i,ifphcbidden, 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 ; pbru7;az 8yva $6d$ 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 striking tf:(mu/i mp0q /rdsy6 whe face of a/ p6/fmmru:iwd0 sq(y $33.5$-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 ha+,o k50zwyxic vec,yzo5w k i0x+ $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff w .ab7f9d/wo0) bkv qgqr7-l xozts y;qi s5/*gavelength $\lambda_0$ 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 wavelengthd0 dvue9a0 wbp m5s:*;unjrb,w4g9va emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength for an+ h+1yqu3pq or $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelen y v3)ur.grdyn1p;0czl/c y q0gth 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 mb0x)wa uc.oki/p ro 46aterial is bombarded with electrons. The wavelength of the ) kioacxb0u4 wo/r6.p$K_\alpha$ 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 detachewn:ffdy/ b-a6d 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 lab might have a podezl 0/ zutm//wer 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 diffracyg/x w.sg xubq,/zn+ 7zfz. 6mtion if the beam emerges through+mz, 7z6bsfwqnu/ zx xgg./. y 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 He-4haq9s x1k6c)9n /4kushxith Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimats2)jaqw4h6ci e 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 cq4hia)2w 6jsanywhere 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 thevo7 qrsr;wq0. 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, estimabjvk4a)iy*os-qjzui3u,,qaz *rt9 5te the average dv*,at*q i5 zi-3)sjybq j4roaz ,ku 9uistance 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 ypef0 e(; /.w swi:cc8ph u7fd$95 \, \text{kV}$ 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 (bindi8,wfhx vp 04zqng) energy of the outermost 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. Below) can b p9v dx.zi4bt +yd1 kr((jffs1e 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 (- xnnm+yov8n l 4b6fiof 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 saabcix u)lr5ndp510s k rb-8;tates possible for a given value of b )1b8ra;c0xpl-uidr n55ka s$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with ek ei+iglxb1m*y qc,+5h.u-p /8nw uoanergy 45 kV is shot through two narrow slits in a barrier. The slit/kgc85xp-lw ,a i+ qmb* eouu i+n.1hys 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 modn da o-y3iio)3el and by quantum mechanics. Compare the results yn3o-a idio3) for $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling with a 4+;sk g 7cjxdnxne; va+3j hl;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 lid*kbc+ 1 w)i2t fvvc(hne with a wavelength centered at 488 nm. Careful measurements show the line is really spread ow*2 (hvtbccd1kvif + )ut 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 then directed at twozru 2 0 tv5wbfhlq4e7. slits 0.70 mm apart. How far apart will th5w. ue2vq z04ht rl7fbe interference peaks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, are accelerated across the so :uhbp g(4:p3zmpi5m ame voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, 5 phb3mu: gompi4:(zpfind the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to the r k(gj wn.02n 5f-bbdgdange from 1 to 6, how many elements woud2knbgw j n. 5g-0(dfbld we find in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if your find ni*s r::5mass is 75.0 kg?:frn5is*i nd : $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 linesn .ih(f9xn x2w with one out of every four matching a line frowin9.f (2xxh nm the 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 from the surface of a certain h la*6i6l hcehig5 t51metal when it is bombarded with high energy illh6ch6i a th5g1e5* radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive sp)gch: s+zcn;iread 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.]