Compare a matter wav uh6 p0u8b0sife $\Psi$ 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 mechanics, l nqz(sb ,(x *lv8,ytspartic*ty,zxv8sq (,(bls nlularly the uncertainty principle.

Explain why it is that the more massive an objec :7in)c/ezbogt is, the easier it becomes to predict its future poozgbiecn: /)7 sition.

In view of the uncertainty principle, why does a baseball seem to have a well;-*dtx4xq 3a 9sdhy zylxj8ub/: x.w r-defined xj. 8h4x/sdt*za3xq y b:;-ywu l9rdxposition and speed whereas an electron does not?

  Would it ever be possible to balance a very sharp needle precisely on its point?m. blo -yn7f0s E.0o lfnbsmy-7 xplain.

  A cold thermometer is placed in a hot bowl of soup. Willxs .5mi/4w;e dups.xa-ko6/ cw2sah u the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement was4 2emus /o cswx6k;d-phuaa.xs wi5/. made? Explain.

  Does the uncertainty principle s9 kamtua47wea ;5v /ct eyv22ret a limit to how well you can make any single measurement ofv4a5urt7;9a 2atmw/ eveyk2 c position?

If you knew the position of an object precisely, with no uncertainty, how well w ppr:swrcs;* 3cea:t4 ould you know its momentu4rc3rs wt ea:;:c ps*pm?

  When you check the pressure in a tire.mug0a*ly i01iu fn 64fk8ux8q0w( ; adkguod, doesn't some air inevitably escape? Is it possi1.xy i fu0umo*kiqn; a8k(g0 af4gl8w06u dd uble to avoid this escape of air altogether? What is the relation to the uncertainty principle?

  It has been said that the ground-stat kz8x2 2p:tncke energy in the hydrogen atom can be precisely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent kz :t 8kp2ncx2with the uncertainty principle in its energy form? Explain.

Which model of the hb z pw.v))qar3ydrogen atom, the Bohr model or the quantum-mechanical model, predicts that the electron spends more time ner .p)v )3qwabzar the nucleus?

The size of atoms vau)q:2qrnyp6jfr f+ mg h470a tries by only a factor of three or so, from largest to smallest, yet the number of electrons varies from one to over 100. ryjnrq) f fht6q4mu+ga:720pExplain.

Excited hydrogen and excited helium atoms both radiate light as they jump down f7kq6kt63sema hk9m + to thsqk e kh a696m7t3+mfke $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no electron spin1 zjr+1(ty /m+yt *pc9ich lqc but otherwise quantum mechanics were valid? Consider the first 20 elementtyrp/ q+c 9(1*zth1jc +mylcis or so.

  Which of the following electr 7r7/cyz;comnon 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 for a uraniu (q-rcma1dc+ tm atom (careful scrutiny across the p ct-r(d+ amcq1eriodic table on the inside back cover will provide useful hints).

In what column of the pf 6 :u3doxcwc2eriodic table would you expect to find the atom with each of the follo6dfcco2 3wx: uwing 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 ex0dwv gxiitp 59e1 1wg3hibit similar properties?

Explain why potassium and r4 )6rz2 ch3x)g xbhjisodium exhibit similar properties.

The ionization energy fl/ign9q 1mfwz 5s 9exi3 j/5bnor 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 wavelength in (Fig. Below) imply a mvtlem y):( ys2t*l4y photon nature for light? :l)lyte m*y2mvys (t4

Why do we not expect perfect agreement between measure5mhg42n1mfd,)mfy x ed values of X-ray line waveleh2 4,g5)1d myfmexnfm ngths and those calculated using Bohr theory?

How would you figure out which lines in an X-ray spectrum correspond to;*oxqekt p:+zfq) 2ilds*5n i $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron trinuqs )x(jf3 9ansitions deep within an atom to produce shorter wavelengths than transitions by outxqsu 3f9ji()n er electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? Howfzg v.iyn5:9h-3 zlu a is it the same?

Explain how a 0.0005-W laser beam, photographed at a distance, can sew6(zw q7,auv*br8esmem much stronger than a 1000-W street lamp uv e8sr7 ab(*6zwmq, wat the same distance.

  Does the intensity of light from a lase 4b,-x:u cjzmralxm4r* ud98br fall off as the inverse square of the dilb*r:x r9xd j , z-mcb4a8muu4stance? Explain. ----待选择----yesno 

  The neutrons in a parallel beam, each having kinetic energm:6y ,p1gp dgty $0.40 \, \text{eV}$ 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/;6zv9eyl1jyc 4 zg o.vu3tza 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 u4a(.ezs4o( uvdcu;xj7 whbg +4yo(s 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 ato /:n*yiiedj)y m 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 thym+gqpe; b/rgt5 *r *ye 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 pq57 odchbk:x,ep+.)ksuht, cossible energy of a neutron contained in a typical nucleus of radi5. , xks7h:qpbeh dk)u+ oct,cus $1.0 \times 10^{-15} \, \text{m}$. [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 tm p8- tnt pta g8gyqi+ahq*)*9o show that if an electron were present in the nucl8p pgmq y 8n*it-t*a9)q+agt heus $(r \approx 10^{-15} \, \text{m})$, 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 positi8h,, gngbp* +f1niqjkbc 9i-won 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 cb5vvo2j +e t1be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an rlhe t0mf/ k;b q9/ugw/75irr-; nohgelectron whose principal quantum number io;0ln5ukh r rr ;9/i7-/ efh/bmqgwtgs $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state of kqeb25b +fpzr( sq*r 1mio/+q
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the gr,6b falb mje16id+ dt6ound state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atot/( jjw yf/if2kv /o:x xb+gy*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 momyt7cczzp 5 3h9entum 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 hd:b-/3hcznc j as $m_l=-3$, 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 1u xt)cvc7n t688 electrons in a "g" subshell.    electrons

What is the full electron configuration in the ground state for elemenx:lz3fqfho+ )a*( f:i xsm n0fts 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) selenium (Sem)j hen1go(ew 1 p4,mm), (b) gold (Au), (c) radium (Ra)? [Hint: see the pepmhwo1 ,4 (g je1m)mneriodic table inside the back cover.]

  A hydrogen atom is in mbbfl g 5i79n6the $6s$ 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 tl+0qcw0wr ;z4kvxw. 6t 63*iseiarvbxfy 3 z2heory. [Hi e2;wxz + *vt3vc3wfqi06kabz6irxlr.y4sw0 nt: 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 zero mf1:5se)w* jwv 9hscj42d pj 9yh,g y .hfa.zafor a filled subshell.

  For each of the following atomic transitions, state whether the transiti-oe xao) y3xhl8n: g/pon is allowed or forbidden, and if forbidden, what rulex 3ox en:glhopa-y8)/ 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 /3z7equ eoe wn(xw.f n+6se+my jy n05a $6d$ 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 stq6/e5mhvxg uo :qwv*8u3x u*triking the face of 85v/uh:q* te *omxux3wqv6g ua $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremss+gp1v;jiti i5 trahlung X-rays emitted from an X-ray tube haveg5itij;1 +vip $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff uq vq lh4-a0a*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 wave) )87ef8z6xdh t hyu5shl bkj6 wb8b3plength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelenjb2mw4xso+y8 i7 2 r a+ gl2+sw9ab-annybk 7fgth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the waveq(i(wkorj*mf. r0-po length 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 yh( yayna76wg0 ;fe 60oevff/ an unknown material is bombarded with electrons. The wavelength y7hwg0 ;6ffy0ay( envf eoa/6of 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 retinas puts oc4/ny sno 1jjb80esv) ut $28$-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 lm;a .biec-u3 uab 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 bfy : f4y;mpzm0eam due to diffraction if the beam emerges through a 0yf4;fyz: p mm$3.0$-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 wavelength7/ s (lsh d5c5b.vhju 31rmkkq of the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncerta 3 h6kzeb q446z38aplue8lij xinty 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 and zero.] How does this result compare to the Bohr3 z6lpb8qz4x4jiee6lukha 38 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 angular mombs6a+4vn76 zrm ei;slentum $L$ 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 z38 u:ke1f+gq2asxvu electron orbit, estimate the average uf1+gu2szae x:q38 kv distance 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 operatecypz. lf,1zy1 s 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) enerthn ke, rnb,2i25 )sfzgy 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) e:ru2z;l9b 4udj f y1jcan 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 numbeu3 m(lhj1jnh0 r 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 of different eleco:2n4 q ;jpxcbt5g 3y ur)-uhctron states possible for a given value of yh5jbnu;tpgo- r2) c4cq3ux :$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons fe: m,, zpoho 0bqi(+pwith energy 45 kV is shot through two narrow slits in a barrier. The slits are a distance ,+,(em pz ih:of b0qop$2.0\times10^{-6}\ \text{m}$ 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 mod+gcla 5veft4df,l0/ wel and by quantum mechanics. Compare the results fofvtl le05 fac4+gw/ ,dr $L = mvr$.
$L_{\text{Bohr}}$ =    $\hbar$
$L_{\text{QM}}$ =    $\hbar$ or $L_{\text{QM}}$ =    $\hbar$

  An 1100-kg car is traveling wit8hwr)poz 6/k56 cx eczh 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 g 3g9a/anbu/wnm. Careful measurements show the a9augn/ /wg 3bline 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. Thta-w: irk7kts. dq(t9mw68 seey are then directed at two slits 0.70 mm apart. How far apart will the interference peirwk8a6(7-dst: et.sm qtw9k aks be on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each inituikyin zf(d u 091tic-ua3,4kially at rest, are accelerated across the same voltage. Assuming that the uncertainty in their position is given by their de Broglie wavelength, find the ratio of tktki ,fdu in1( zuc0 4yi39au-he uncertainty in their momentum.

  If the principal quantum number n wq m8oi6gi)a- qere limited to the range from 1 to 6, how many elements would we fg- qm8i6ao)q iind in nature?   

  If your de Broglie wavelength were 0.50 m, how fast would you be moving if yonl5v1n62xf f qur mass islnqvn2x 5f 6f1 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 with on cvh/cu jrq. eh+dxkx *c;+nd-hg8b/0e 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 electron, determine Z and thejg+/bnv0xh-*q+8 ./eu hdd cxhc kc;r element in question. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted from th- qrofk gk(5)pe surface of a certain metal when it is bombarded with high energy radiation. If this photon wavelength correq)of p(krkg -5sponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spread of a laser beam,p*l21uwe:g 4 j id8ybm $$\theta \approx \lambda/D$$ , 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.]