Compare a matter waveboq)w ufd::z.,p (cau $\Psi$ 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 quarkv;+n *pq,4 sh/errmntum mechanics, phq+ *prr/rs4n ;vemk ,articularly the uncertainty principle.

Explain why it is that the more massive an object is, the eas ev,cr (l2o,pqier it becomes to predict its future posip,rl2 ocvqe( ,tion.

In view of the uncertainty principle, why does a baseball seem twgm+a23q *v b.4gwnla o have a well-defined position and speed whereas an electron does not?2vg+.3n 4abma lwq*wg

  Would it ever be possible to balanc0.qsiv q oj 97ku+,cefe a very sharp needle precisely on its point? ie9 s k+v, 7jqocq0.fuExplain.

  A cold thermometer is placed in a hot bowl of sz0srj: 0vph*3* tdxjy,prr+v oup. Will the temperature reading of the thermometer be the same as the temperature of the hot soup before the measurement was made? Explain.xd0t0j*h 3v rz:+rpy*rpj v,s

  Does the uncertainty 4amj4 1myn6ub principle set a limit to how well you can make any single measujmu ny4a1b4 m6rement of position?

If you knew the position of an object precisely, with no uncertainty, how wellm c*nah *w -w)twl*)qn wo*h )lq wnwnt-mwa)*c *uld you know its momentum?

  When you check the pre obk1hcub8*,mssure in a tire, doesn't some air inevitably escape? Is it possible to avoid this escape of air altogether? What is the relation to the uncertainty princobm c1 ,bh8ku*iple?

  It has been said that the ground-state energy in the hydrogen atom can be prec nf hgcyyuy8qpfp7 j bglcst37(*w 37*t3zd2( isely known but the excited states have some uncertainty in their values (an "energy width"). Is this consistent with the uncertainty principle in its ene y72yc3cfp7 gfq dnstu3bhp7tyg(( 8l3*j *zwrgy form? Explain.

Which model of the hydrogen atom, the Bohr more +1)pg cw t6k2-mwqodel or the quantum-mechanical model, preqpr -ot6) mwe c21wkg+dicts that the electron spends more time near the nucleus?

The size of atoms varies by only a factor of thq19d -k-evqg j9kodl(ree or so, from largest to smallest, yet the number of electrons varies from o19vkqd (j- gked-o9 lqne to over 100. Explain.

Excited hydrogen and excited helium atomsuz3 y n 1fs8rnd:y5)ex both radiate light as they jump down to thy zs531df :eyn )xu8nre $n=1, l=0, m_l=0$ state. Yet the two elements have very different emission spectra. Why?

How would the periodic table look if there were no h. yp hg0st(g;electron spin but otherwise quantum mechanics were valid? Consider the t0yhg;pg h.s( first 20 elements or so.

  Which of the following electron confhrv4afd rzi)nu+ 8(+gigurations 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 uranium atom (careful scrutiwdb *d pkt:3u.ny across the periodic table on the inside back cover will provide useful hint.:dbwtpu*3 dks).

In what column of the pe)r1 j(zgf: ja5g h j*u(/fiksyriodic table would you expect to find the atom with each of the following configu( fr(kj:yi*) 5auh/z1sgfjjgrations:
(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 prrzps (fsijbxr/1 6qn:fl *5h:operties?

Explain why potassium and sodium +5pj8o q7j szi*,pwcqhq.fq- exhibit similar properties.

The ionization energy for 1:df lhoeyrb1. im *zf2*ljh 3neon $(Z=10)$ 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 lin*khjl:b:q kyx a.tc s12/ 1teght? clet.*2sna k 11yt :/bqjh: kx

Why do we not expect perfect agreement betweei1mae*i/3t woe63 n2akpr9n z n measured values of X-ray line wavelengths and those calculated using Bohr t/6 pzaknei3e*w93 1toman 2 riheory?

How would you figure out which lines in an X-ray spectrum correspond to 1g/ o-9:ln tn:ztsmna $K_\alpha, K_\beta, L_\alpha$ etc., transitions?

Why do we expect electron transitions deep within an atom to produce short*iwitt-( ws zeyo9t *.er wavelengths than tra-(s* itw tei.*ot9wzynsitions by outer electrons?

Compare spontaneous emission to stimulated emission.

How does laser light differ from ordinary light? Ho3tis,k(p/d l d2*sf 7omjwr e rhl-5/mw is it the same?

Explain how a 0.0005-W laser beam, photographed/2h8o* zxs*ip vo9-ay z 9erik at a distance, can seem much strong/y2a oh *98s zip-*o9xekrivzer than a 1000-W street lamp at the same distance.

  Does the intensity of light from a laser fall off as the inverk g3i gc0z.op39)n kokse square of the distance? Ekz3 ik 9kcg3on)p g0.oxplain. ----待选择----yesno 

  The neutrons in a parallel beam, each 8cbom3hk,:pi:c / s jwhaving 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 k;oqwsa7pi pt *6h(+rwith 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 mea)xf2 fuzzrp* uxsl9*;0ky f8p sured 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 typ. b8zl7*ndxoy 21ryvckqv0 ) dically $10^{-8} \, \text{s}$. 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 fcp5 0e 4ty* oht3)owumass 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 energy of a neutron con (sfp:xr:qw74skcs h ,tained in a typical nucleus of radiuc4s(sfq,x7 :phksr : ws $1.0 \times 10^{-15} \, \text{m}$. [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 th sexcl,t:)/m c :5varc 2ul9fqe nucle:qa2clclvs ,c xt9 mur)/5f:eus $(r \approx 10^{-15} \, \text{m})$, 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 ) 81xg9v xnvi c6de-mfa $3.00$-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 canu2fnp0 );8j ).a uxelj o6 viwyki4cx+ be in the $n=6, l=3$ subshell?    elections

How many different states are possible for an electron whose p5sybz vb 6m3,e 7unk8fe h85jirincipal quantum number is fe8 7, jbsnm8ybvhezku5i63 5 $n=4$? Write down the quantum numbers for each state.

List the quantum numbers for each electron in7 bhpgx a* tjw;/h7d0y0fk;im the ground state of
(a) carbon $(Z=6)$
(b) magnesium $(Z=12)$.

List the quantum numbers for each electron in the ground styc6. yfqrqiaja-)1 9 wate of nitrogen $(Z=7)$.

  Suppose a certain hydrogen atom ha.zpcl 4e5gwfiv51l , qs $l=4$. 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 momentu(bpa kn2: w z1b6g7lacm 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 ha j2;ou 8lj-zfra b7z-q,sxi-4h(sq ygs $m_l=-3$, 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 elecf. a/irj u+jy ngrldk : eq3/)sobi207trons in a "g" subshell.    electrons

What is the full electron conygjo1sn o6sh,5s:m20ev xzr )jvk131pi ymd;figuration 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 configureo*i hh*) nzxu5ct)rmn 9/ qm-ation for (a) selenium (Se), (b) gold (Au), (c) radium (Ra)? [Hint: seeh* -ex nut*imq n/r9mzcho 5)) the periodic table inside the back cover.]

  A hydrogen atom is injgxg- 4 6m c7/m.4pz6eflvvxnnhsn f.w9 x++o 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 tr42-w2 2ag/s 2nzi)ni ydj pjfhe third electron in lithium using the Bohr theory. [Hint: This elf4in/jp gzrdas 2)2 i2j-y 2nwectron 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 zq 6ehw:chfzt )h36k d;ero for a filled subshell.

  For each of the following atomic transitiony84 6rddhsa1m s, state whether the transition is allowed or forbidden, and if forbidden, what rule is being violated4 mhasr8d16dy :
(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.u yozy*uy1tpa d4z*4 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 emitvlt8ndh2. 2zjbiupnhvvk6y)1/d. 8tted by electrons striking the face of akh td1 6. u)nbp2ythz 8/l8.ndvjv2vi $33.5$-kV TV picture tube?$\lambda$ =    nm
What are the longest wavelengths?   nm

  If the shortest-wavelength bremsstrahlung X-rays emitted from gloe:j6th3v 6do0l+ rm /m 2bran X-ray tube have6 / em0vl rh:tmol3rdbo2 6jg+ $\lambda=0.030 \, \text{nm}$, what is the voltage across the tube?    kV

Show that the cutoff wavelengthq6zlhn09 -lcxpwm4;w $\lambda_0$ 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 wavelength emitteivi.tm3oauv4f :z1+o d when a Co $(Z=27)$ atom jumps from $n=2$ to $n=1$.
$\lambda $ =    nm

  Estimate the wavelength foyd w( bfa3af-h3 5fd6ur an $n=2$ to $n=1$ transition in iron $(Z=26)$. $\lambda $ =    nm

  Use the Bohr theory to estimate the wavelengt.l 8h 1.f6g pwc;qkb 15vzhup:xcv(v ah 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 isjzy,)ckb b4:hem 3oc* bombarded with electrons. The wavelength ofj )c*hm3kbcz ob:e,y4 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 detacheds 0re+ n5gfn2g 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 r8/ tfmh8gzn2 lab 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 spreadtrdg4;8 ry6 ml4l.ht fjod8u6 of a laser beam due to diffraction if the beam emerges through athfrd;l.r 4ut8j yo6d4m 86lg $3.0$-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-N9k h,/ wyy4(obv dkyh;o1 poe-e laser?$\lambda $ =    nm

Use the uncertainty principle to estimate the position uncertainty for the elax9w3p63o lng ectron 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 Bohpl936ow 3 ngxar 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 m0m,lo vmxh( lxq13*u 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 radiu /nd, pg)5oriqs of an electron orbit, estimate the average distance from the nucleus for an electron r/ g )nido5,qpin 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 p 7ep 9e1h uaf2lemgro: :3)yhat $95 \, \text{kV}$ 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) ).3h)-utol.ia u zju w-lm7usenergy 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 z6;,av cnmjud* u.01qto a;jge 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 s(thww)g 7i 58vxv0sn 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 states possible t6s3 qne cj; uk9 b7l iptxu;c.6h2c6qfor a given value of hci.xcttkuu63lq cq2n9; e7;6 psb j6$n$ is $2n^2$. (See Problem 50.)

  A beam of electrons with energy 45 kn53 p 9ssr(3uzlax cww7h ma6(V is shot through two narrow slits in a barrier. The slits arnx7s ha az336r (wp(wc5mu s9le 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 thelklid8telv6 6 p:-3p h Bohr model and by quantum mecha- 6hti:dp plklv8l 6e3nics. 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 spee9ch7,(zqyi f- epjn( kd 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 cont2o3+ wdrbn5 yfains a line with a wavelength centered at 488 nm. Careful measurements show the line is really spread out between 487 and 42bnr fd y+ow5389 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 two slzbkbf5f7h , -cits 0.70 mm apart. How far apart will the interference peaks be on - cbb,ff 57hkza screen 28 m away? $\Delta y$ =    nm

An electron and a proton, each idx p6:fz2hi (gnitially at rest, are accelerated across the same voltage. Assuming that the uncertainty in xfdz 6:giph 2(their position is given by their de Broglie wavelength, find the ratio of the uncertainty in their momentum.

  If the principal quantum number n were limited to9 q9g 4 a7*hp:uzefrhc the range from 1 to 6, how many elements woul p: 9*ehqazgcfr7u94hd we find in nature?   

  If your de Broglie wavelength were 0.5 lm 2;: o,cz0px9hxtqcgweqo)7 h 13dv0 m, how fast would you be moving if your mass eqptwz 9 d )o7,q3c: m0g xvx;olh12chis 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 li a 756ch g eiuur5oi0tj4c:.hlnes with one 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 the element in qhcjl uo0:irhai46gu te55. 7cuestion. ----待选择----lithium berylliumboron 

  Photons of wavelength 0.154 nm are emitted fromiz-5 ww7 j d)qv1xlh-z the surface of a certain metal when it is bombarded with high energy radiation.wj7-w)i1x v-zhd lzq5 If this photon wavelength corresponds to the $$K_\alpha$$ line, what is the element? ----待选择----nickelcopperzinc 

Show that the diffractive spreabc6:bqnc0 vpxkx 7*uv- om )6dd 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.]