Compare a matter wav7umz (gx1nc ,yvn0lq1 pu/g(a e $\Psi$ to (a) a wave on a string, (b) an EM wave. Discuss similarities and differences.

Explain why Bohr's the6mh-d ih 0lh8wory of the atom is not compatible with quantum mechanics, particular06hlm8 h wih-dly the uncertainty principle.

Explain why it is that the morre3v,0c :(/ivx 2vywqjj1 d qle massive an object is, the easier it becomes to predict its future position j:(vv2,iqlqr3j01xcw v/yde .

In view of the uncertainty principle, why does a baseball seem to have a well vn; up8(.ppcl-defined position and speed whereas apcv8 ;lpu.p (nn electron does not?

  Would it ever be possible to balance a very shar as8f;0 (icutqmn8l+gp needle precisely on its point? t8ugc8l;m0 (+ nifa sqExplain.

  A cold thermometer is placed in a hot bowl of soup. Willhhyj 1dq t 2zk6a2v1,d( uae/h the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement 1h kde2(jt2 ya/au6v, zhdq1hwas made? Explain.

  Does the uncertainty principle set a kdo 9g,k82cxe limit to how well you can make any single measurement of posg,k92kcx deo8 ition?

If you knew the position of an object precisely, with no unc0k,bdj su2lu *ertainty, how well would you know its lds 0 ju*b2,kumomentum?

  When you check the pressure in a tire, doesnx ,pr1z7ll08xcktw)lx 6 2qy j't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertaintjlpy8 r16l)q c,x klxw702zxty principle?

  It has been said that the ground-sti nt-- qj,(nyp*unj6scfyz+k( e+g a( ate energy in the hydrogen atom can be precisely known b(y j kes(ug 6jan*cfzn-n q-y+,t+( iput the excited 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, th(k*h7axm *jyn e Bohr model or the quantum-mechanical model, predicts that the electron spendyxm**n7 h(a jks more time near the nucleus?

The size of atoms varies by only a factor of three or so, from lar ppb2 jxt:lmo-c6 zy-9gest to smallest, yet the number of electrons varies from one to ovc m--:plop2xt9bz6 jy er 100. Explain.

Excited hydrogen and excited heliuy fg8 ) (h+r.pizd-hpcm atoms both radiate light as they jump down to thec.p8dzhig)+ (hf -pr y $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no egx ihkt 9* *l0(ss at+9rkpkb 8q-o.ealectron spin but otherwise quantum mechanics were valid? Consider the first 20 s ke9.ptaxti 8 -*g0os9+(h q*kalbr kelements or so.

  Which of the following electron configurations are not allowedsi .2m1t dbdgf)-ee1v :
(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 (c(jlaxtuld 0*7areful scrutiny across the periodic table on the inside ba dx uj7a*0llt(ck cover will provide useful hints).

In what column of the periodic table would you expect to find the au pvhg :/t76yttom with each of the following 6/ y pt7ghvt:uconfigurations:
(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 sim3jv.u d7s1 *r/exhpr qilar properties?

Explain why potassium and sodium exhibit 4sii ieigy0bv4 0):dt similar properties.

The ionization energib9(h csy5xkq.3 x 1cny 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 wavelength in (Fig. Below) imply h6.b k ez/qvvq9)bhqs1er*/x a photon nature for light? e)ke 6 *1 bq9/vqhrxq/. vhzbs

Why do we not expect perfe.9+u5 c wunf3(jiyx vhct agreement between measured values of X-ray line wavelengths and those calculated using c yujiu3(x5+.hvnw 9fBohr theory?

How would you figure out which lines in an X-ray spectrum h 5-xjbwf,wq e3 l i1ao.n3q.-zz ku5mcorrespond to $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to prodi2 i-(l:dekr autf6- a3fp:wcuce shorter wavelengths than transitions by outef-::pa2taefki u6rd l (iw-c3r electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordicp40fa7b17x 5+r g cgeoyobif( im.l- nary light? How is it the same?

Explain how a 0.0005-W laser bhc3i3lag4 7kij8 -sjceam, photographed at a distance, can seem much stronger than a 1000-W street lamp at thi4j8iskca hl3c37 j-ge same distance.

  Does the intensity of light from a laser fall off as the inver.8 pdvk74 as;qv9xo gv,qnzv/se square of the distance?g,vxpvq ;/qk8 sondz va4 9v7. Explain. ----待选择----yesno 

  The neutrons in a para 2qnp:qni* joi8xu z:/llel 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 travelinb/jswz/(wdkj egy.,bb, ju/ 0g with 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 measuredet15jn x ja58qz7s8vv 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 i e62pgr5o9njw n an 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 uncertai6 ky;p y3gazp2 f+*ajmhf*)d,esl wf/nty in 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 possible ener+mlr i2l79w argd +;irgy of a neutron contained in a typical nucleus of rdwi+ mrr2a7llg+i 9r;adius $1.0 \times 10^{-15} \, \text{m}$. [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 :1vii;y4i.*qyg vr ga in the nuc4viy i1:a *;qyvgrig.leus $(r \approx 10^{-15} \, \text{m})$, 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 t/ji2n9gy1g ryx e5ir4 he position 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 wz -qi*)rn-xsc4ai 3qin the $n=6, l=3$ subshell?    elections

How many different states ame;r bj 3lx-jxe) ) .xnhm-f6qbb,k2j re possible for an electron whose principal quantum number is me-bbe.))rnmqxx3fj, x- l kj;j6h2b$n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in the ground state oi;aj lxgx1b04 of07ayp 3 x8qqf
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electrojk 1 9)foa0mx:l0 ffzvn in the ground state of nitrogen $(Z=7)$.

  Suppose a certain hydrogen;yx5o:u*cmb, 2u da8naeb q3 fv4qa p7 atom 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 momentumjiljzx6;) x:e 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 ;ghc y6j1 j((a 4urcpo$m_l=-3$, 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 electronsf0d -syx ;/w:z8ig*zk-e sk vw in a "g" subshell.    electrons

What is the full electron configuration in the ground state for elem x 0sryem62u8yents 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 (Se), (b) gold,ah(wf7xd r +w (Au), (c) radium (Ra)? [Hint: se+w, wax7fh(rde the periodic table inside the back cover.]

  A hydrogen atom is in thec ernw+;hqj- 2hr.s8s (g e5xi $6s$ 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 e 0t2)hthurbr)px* z7 blectron in lithium using the Bohr theory. [Hint: This eleu rxrpt) b 7tz2)h*0bhctron 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 mo8*-va1 woapnav3,lqa)c c4g pmentum is zero for a filled subshell.

  For each of the following:e:8s9 :)82ku htyzl skrkd hq atomic transitions, state whether the transition is allowed or forbidden, and if forbidden, what rule is being 8s k2ehh:r z:)qkdyk:9 8us tlviolated:
(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 a fvr8g,h8 o)g9rl yxy3 $6d$ 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 thedj 8i ij6/sj 5;fhdhp/v,yqfo1 xco- . face of ai-hpqsjf6 cd.jj ;if/1y 5v8h/oxod , $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlungcgj:w21en eb)az2e,.t6f nce X-rays emitted from an X-ray tube haveezn efne:t 1e.a2bj)2c6 , wcg $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelpa 9 eekipovh4lc8 1,/ength $\lambda_0$ 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 wa zm;jmk9oj+ b0velength emitted when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelenxc,e, mc 5hib/gth for an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estim*o y)t aq1pqw.ate 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 unknoszl;5k6f8q,go o2 i t9 ,grrcjwn material is bombarded with electrons. The wavelength oft q 6 i9r,lgos25zc8;,fogkrj 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 xm54at-sf4)r zt.6 j1d ug wpy*rdbl)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 z66ui8 * fujbtpower 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 diffrac 1ob;oy+v+i ax/ ryxv/tion if the beam emerges thro/ ;y+ooy1x+aix /vrvbugh 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 wavelengthownriu .7s*b . (9ig4 +toqizg of the He-Ne laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position unw e)tvx m lgzuuw3a;.m, 05)jncertainty for the electron in the ground state of the hydrogen atom. [Hint: Determine the momentum using the Bohr model of Section 27-12 auetwx,v. m;a 0uj3)w 5nmgl)znd 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 smallest possible values for the angular mome : v,5nldbcqdaot 6ta./ty5m 4ntum $L$ 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 fopc+bf wz //h,eka 40 zkqye/t0r the radius of an electron orbit, estimate the average distance from the nucleus fbw,z//qk0a 0kz4e /h+ tepycfor 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 /d(t8t5 f kvxu -*so7y1y iqby*kv lu,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 (hqgibv y:8o( 3qkfx/ nb3kl1$8.26 \, \text{eV}$.
(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 tha ,vx1rh4o kk/ ,qkl*nct 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 number9.yi ce r/ubu7lfw 4z- 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 electron j8 b hl j4l.chvdcb(j-)c4mb4states possible for a given value of l4j 4 mjlhb h.4cb8- d)b(vjcc$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kV is shot through two narrow slits i qvezv9 y/n hun 74;m*w)sr4ssn a barrier. The slits are a distance /evs94qh)u4 nr syn m7vs; z*w$2.0\times10^{-6}\ \text{m}$ 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 xvp*d5acpury r 2d km,vy6f/v*z(:5z the Bohr model and by quantum m(d* py p5r5a v vr:u*z,fd62vzy/cxkm echanics. Compare 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 sp8dkb ).-0 f)tkz nx7wrm4enlu eed 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 centereddo-(1 sls,2tflwd;iu e sx7*q at 488 nm. Careful measurements show the line is really spread out between 487 and 489 nm. Estimate the lifetime of the excited state that pro ssildl,xs *7fe ;w(-1odu q2tduced this line.
$\Delta t = $    $\times 10^{-14}\ \text{s}$

  Protons are accelerated from rest t yk(,nr ya7z+across 550 V. They are then directed at two slits 0.70 mm apart. How far apart will the interference peaks betay +y(,7nrkz on a screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each initially at rest, as6zha)au fb0f j0u34are accelerated across the same voltage. Assuming that the uncertainty in tfbsuf h3j6u 04aa az0)heir position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n werj6qm3vk0s4 kt e limited to the range from 1 to 6, how many elements would we find in nature? q k0js4 36mkvt  

  If your de Broglie wavelength were 0.50 m, how fast woul0v;4kgjw *suirfd* b. d you be moving if your mass is vd**s fwru.4gjbk i;0 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 seriewr; fmnrai;6)s of lines with one out of every four matching a line from the Lyman series of hydramwf n );ri;r6ogen. 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 oo 3*dsa;:zn(rxj jr /of a certain metal when it is bombarded w/z: ;aojs3j dor(r n*xith high energy radiation. If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractivel.ot+qq7rc7l spread 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.]