Subject : CHEMISTRY Topic : Atomic Structure

20 Pages·2011·0.58 MB·English

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Subject : CHEMISTRY
Topic : Atomic Structure
R
Index
1. Key Concepts
2. Exercise I
3. Exercise II
4. Exercise III
5. Exercise IV
6. Answer Key
7. 34 Yrs. Que. from IIT-JEE
8. 10 Yrs. Que. from AIEEE
Student’s Name :______________________
Class :______________________
Roll No. :______________________
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Physical Constantsa e
r
u
Constant and Symbolb SI Value Gaussian Value ct
u
Speed of light in vaccum c 2.99 ×108 m/s 2.99 × 1010 cm/s str
c
Proton & electron charge e 1.60 × 10–19 C 4.8 × 10–10 statC mi
Permittivity of vaccum ε0 8.85 × 10–12 C2/N-m2 Ato
Avogadro constant N 6.02 × 1023 mol–1 6.02 × 1023 mol–1 0
Electron rest mass mA 9.10 × 10–31 kg 9.10 × 10–28 g of 2
e 2
(0.000548 amu) e
g
a
Proton rest mass m 1.67 × 10–27 kg 1.67 × 10–24 g P
P
(1.00757 amu)
)
Neutron rest mass m 1.67 × 10–27 kg 1.67 × 10–24 g P.
n M.
(1.00893 amu) (

Planck constant h 6.62 × 10–34 J s 6.62 × 10–27 erg s L,
A
Permeability of vaccums µ 4π × 10–7 NC–2 s2 P
0 O
mBohr radius a 5.29 × 10–11 m 0.529 × 10–8 cm H
o 0 B
ses.cBohr’s velocity 2.188 ×106 ×Zn m/sec. 2.188 ×108 ×Zn cm/sec. 81 ,
s 8
la Z2 58
kocBohr’s energy –21.8×10–19 n2 J/atom –21.8 ×10–12erg/atom 30
e 9
t 8
www.(BG–oa1hs3 rc. 6mo neasVgtna/aentttoonm()BM) Rβe 89..32174 ×5 1J0/m–2o4l -JK/T 8.3145 × 107 erg/mol-K 00, 0 9
e: Boltzmann constant k 1.38 × 10–23 J/K 1.30 × 10–16 erg/K 0 0
bsitGravitional constant G 6.67 × 10–11 m3/kg -s2 6.67 × 10–8 cm3/g-s2 2 0
e 3
wEnergy Conversion Factorsa )-
m 1 erg = 10–7 J 55
7
o1 cal = 4.184 J 0
r (
e f1 eV = 1.602177 × 10–19 J = 1.602177 × 10–12 erg = 23.0605 kcal/mol H:
g P
kaGreek Alphabet r)
cAlpha Α α Beta Β β Si
PaGamma Γ γ Delta ∆ δ K.
y Epsilon Ε ε Zeta Ζ ζ R.
udEta Η η Theta Θ θ S.
StIota Ι ι Kappa Κ κ A (
ad Lambda Λ λ Mu Μ µ RIY
oNu Ν ν Xi Ξ ξ A
l
n K
owROhmoicron ΡΟ ρο SPiigma ΣΠ σπ R.
D G
Tau Τ τ Upsilon Υ υ
A
EPhi Φ φ Chi Χ χ H
E U
RPsi Ψ ψ Omega Ω ω S
F r :
o
t
c
e
r
Di
S,
E
S
S
A
L
C
O
K
E
T
KEY CONCEPT e
r
u
STRUCTURE OF ATOM uct
r
Rutherford's Model st
c
Bohr's Model mi
o
Wave mechanical model At
EXTRAE lNecUtCroLnEsA,Rpr oPtAoRnTs & (e n−−−−e )utrons are the most important fundamental particles of atoms of all elements 3 of 20
e
(Except hydrogen) g
a
P
Some uncommon Fundamental particles :
1. XA , A = Z + n
Z P.)
M.
1 1 1 mM (
2. Reduced mass µ=M+m =m+M m = mass of e– ; M = Mass of nucleus L,
A
P
h O
m3. Photon is considered massless bundle of energy. But to find its mass use m = H
o λc B
ses.c4. E = mc2 , E = hν = hc/ λ = hc ν 81 ,
as no.of molecules reacting 88
l5. Quantum efficiency or Quantum Yield = 5
oc no.of quanta absorbed 0
k 3
e6. R = R (A)1/3 , R = 1.33 ×10–13 cm A = mass number 9
www.t7. 12nmα v1α2 =K Zer.2e1 ; Tan θ2 α b1 0, 0 98
0
bsite: number of a particles at θ = Ksin41θ/2 ; b = impact parameter 2 00 0
e 3
w   )-
e from 8. Rydberg’s Equation λ1=ν=RHn112−n122×Z2 H: (0755
g9. Limiting spectral line (series limit) means n = ∞ P
ka 2 r)
c10. H line means we know n , n (longest λ , shortest ν , least E) [ H , H , H , H ] Si
Pa α 1 2 n(n−1) α β γ δ K.
y 11. No. of wavelengths observed in the spectrum = R.
ud 2 S.
St when e– deexcites to ground state , n = no. of higher orbit A (
d Y
a12. 1/2 mv2 = hν – hν0(w) (work function or B.E.) RI
o
A
nl hc K
ow ν0 = Threshhold frequency W = hν0 = λ R.
D 0 G
E 1 HA
E13. Accelerating potential = eV = KE = mv2 U
R 2 S
F14. λ = hc/E = 1240 ev. nm r :
o
t
Kq q c
15. K= 1 ; P.E. = 1 2 centrifugal force = mv2/r re
4πε r Di
0 S,
E
h S
16. mvr = n· = n.(cid:1) S
A
2π
L
C
E1 2 2π2me4 2 −2π2me4 KO
17. E = z = – z ;E = E
n n2 n2h2 1 h2 T
2 2 2 re
n h z 2πe u
18. r = x 19. v = × ct
n Z 4π2e2m n h ru
st
20. revolutions per sec = v/2πr 21. Time for one revolution = 2πr/v c
mi
22. Separation energy = En∞=∞ −Engiven = 2,3,4,................. Ato
23. No. of waves = n = no. of shells 24. I.E. = E – E (K, L, M, N) 20
n=∞ ground state of e- of
150 4
e
25. λ = h/mv = h/p 26. λ = Å g
Vinvolts Pa
27. E ≠ KE KE = 1/2 mv2 , E = hν 28. ∆x.∆p > h/4π
n )
29. ν1/2 = a(z–b) b = screening constant P.
M.
30. Nucleons 31. Isotopes, Isobars, Isotones (A – Z) (

32. Isoelectronic 33. Isosters L,
A
34. Isodiaphers (A – 2Z) 35. paramagnetic P
O
m H
h
o36. Diamagnetic 37. S = S(S+1) B
sses.c38. µ = n(n+2) B.M. n = number of unpaired e– ; 2π 881 ,
a 8
l39. Radial Nodes ; Angular nodes ; Total nodes 5
oc 0
k (n – l – 1) l (n–1) 3
e 9
t40. Total no. of e– in an energy level = 2n2 8
ww. Total no. of e– in a sublevel = 2(2l+1) 0 9
w Maximum no. of e– in an orbital = 2 0,
0
: Total no. of orbitals in a sublevel = (2l+1) 0
e 0
it No. of subshells in main energyshell = n 0
ebs No. of orbitals in a main energy shell = n2 32
w l = 0 1 2 3 4 )-
m 55
s p d f g 7
o 0
r (
e f H:
g41. ELEECTROMEGNETIC SPECTRUM P
ka → λ increases r)
c Si
Pa K.
y R.
ud S.
St A (
d Y
a RI
o A
l
n K
ow R.
D G
E λλλλ in meters. HA
E U
R Distinction between the wave – particle nature of a photon and the particle–wave nature of sub- S
F atomic particle. r :
o
t
PHOTON SUB ATOMIC PARTICLE c
e
r
1 Di
1. Energy = hν Energy = 2 mν2 S,
E
S
c h S
2. Wavelength = Wavelength = A
L
ν mν C
Note: We should never interchange any of the above and to write electronic conf. of Cation O
K
first write for neutral atom & then remove e– from outermost shell. E
T
SHAPES OF ATOMIC ORBITALS e
r
u
t
c
u
r
st
c
mi
o
At
0
2
of
5
e
g
a
P
)
P.
M.
(

L,
A
P
O
m H
o B
ses.c The spherical Polar Coordinates S 81 ,
s 8
a 8
l 5
oc 0
k 3
e 9
t 8
ww. 0 9
w 0,
0
: 0
e 0
it 0
bs 2
e 3
w )-
m 55
7
o 0
r (
e f p p p H:
g P
ka X y z r)
c Si
Pa K.
y R.
ud S.
St A (
d Y
a RI
o
A
l
n K
ow R.
D G

A
E H
E U
R S
F r :
o
t
c
e
d d d Dir
z2 x2−y2 xy S,
E
S
S
A
L
C
O
K
E
T
e
r
u
t
c
u
r
st
c
mi
o
At
0
2
of
6
e
g
a
P

)
P.
M.
(

L,
A
d d f P
m xz yz z3 HO
o B
ses.c 81 ,
s 8
a 8
l 5
oc 0
k 3
e 9
t 8
ww. 0 9
w 0,
0
: 0
e 0
bsit 2 0
e 3
w )-
m 55
7
o 0
ge fr fxyz f 2 2 fx(y2−z2) PH: (
ka z(x −y ) r)
c Si
Pa K.
y R.
ud S.
St A (
d Y
a RI
o
A
l
n K
ow R.
D G
A
E H
E U
R S
F r :
o
t
c
e
f f f Dir
y(z2−x2) x3 y3 S,
E
S
S
A
L
C
O
K
E
T
EXERCISE -I e
r
u
t
LIGHT c
u
r
Q.1 H- atom is exposed to electromagnetic radiation of 1028 Å and gives out induced radiations. Calculatec st
mi
λ of induced radiations.
o
At
Q.2 The wavelength of a certain line in the Paschen series in 1093.6 nm. What is the value of n for this0
line. [R = 1.0973 × 10+7 m−1] high of 2
H 7
e
Q.3 A certain dye absorbs 4530 Å and fluoresces at 5080 Å these being wavelengths of maximum absorptionag
P
that under given conditions 47% of the absorbed energy is emitted. Calculate the ratio of the no. of
quanta emitted to the number absorbed. )
P.
M.
Q.4 The reaction between H and Br to form HBr in presence of light is initiated by the photo decomposition
2 2 (
of Br into free Br atoms (free radicals) by absorption of light. The bond dissociation energy of Br is L,
2 2 A
192 KJ/mole. What is the longest wavelength of the photon that would initiate the reaction. P
O
m H
oQ.5 Wavelength of the Balmer H line (first line) is 6565 Å. Calculate the wavelength of H (second line). B
ses.cQ.6 Calculate the Rydberg constanαt R if He+ ions are known to have the wavelength differenβce between the 81 ,
s 8
a first (of the longest wavelength) lines of Balmer and Lyman series equal to 133.7nm. 8
l 5
oc 0
kQ.7 The quantum yield for decomposition of HI is 2. In an experiment 0.01 moles of HI are decomposed. 3
e 9
t Find the number of photons absorbed. 8
ww. 0 9
wQ.8 The light radiations with discrete quantities of energy are called ______. 0,
Q.9 What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition, n=4 0
: 0
ite to n=2 of He+ spectrum. 00
bs 2
eQ.10 Calculate the energy emitted when electrons of 1.0 g atom of hydrogen undergo transition giving the 3
m w spectral line of lowest energy in the visible region of its atomic spectrum. 55)-
7
o PLANCK’S QUANTUM THEORY 0
r (
e fQ.11 Calculate the wavelength of the radiation that would cause photo dissociation of chlorine molecule if the H:
g P
ka Cl- Cl bond energy is 243 KJ/mol. r)
c Si
PaQ.12 Suppose 10−17 J of light energy is needed by the interior of the human eye to see an object. How many K.
y photons of green light (λ = 550 nm) are needed to generate this minimum amount of energy. R.
ud S.
StQ.13 A photon having λ = 854 Å causes the ionization of a nitrogen atom. Give the I.E. per mole of nitrogen in KJ. A (
d Y
aQ.14 Calculate the threshold frequency of metal if the binding energy is 180.69 KJ mol−1 of electron. RI
o
A
l
n K
owQ.15 Calculate the binding energy per mole when threshold wavelength of photon is 240 nm. R.
DQ.16 A metal was irriadated by light of frequency 3.2 × 1015 S−1. The photoelectron produced had its KE, G
A
E 2 times the KE of the photoelectron which was produced when the same metal was irriadated with a H
E U
R light of frequency 2.0 ×1015 S−1. What is work function. S
F r :
o
Q.17 U.V. light of wavelength 800 Å & 700 Å falls on hydrogen atoms in their ground state & liberates t
c
electrons with kinetic energy 1.8 eV and 4 eV respectively. Calculate planck’s constant. e
r
Di
Q.18 The dissociation energy of H2 is 430.53 KJ/mol. If H2 is exposed to radiant energy of wavelength S,
253.7 nm, what % of radiant energy will be converted into K.E. E
S
S
Q.19 A potential difference of 20 KV is applied across an X-ray tube. Find the minimum wavelength of X-ray A
L
C
generated. O
Q.20 The K.E. of an electron emitted from tungstan surface is 3.06 eV. What voltage would be required to K
E
bring the electron to rest. T
BOHR’S MODEL e
r
u
t
Q.21 Calculate energy of electron which is moving in the orbit that has its rad. sixteen times the rad. of firstuc
r
Bohr orbit for H–atom. st
c
−21.7×10−12 mi
Q.22 TTTT hhhheeee eeeelllleeeeccccttttrrrroooo nnnn eeeennnneeeerrrrggggyyyy iiiinnnn hhhhyyyyddddrrrrooooggggeeeennnn aaaattttoooommmm iiiissss ggggiiiivvvveeeennnn bbbbyyyy En= n2 ergs.Calculate the energy required0 Ato
− 2
to remove an e completely from n = 2 orbit . What is the largest wavelength in cm of light that can beof
8
used to cause this transition. e
g
a
Q.23 Calculate the wavelength in angstrom of photon that is emitted when an e− in Bohr orbit n=2 returns toP
the orbit n=1. The ionization potential of the ground state of hydrogen atom is 2.17×10−11 erg/atom. )
P.
M.
Q.24 The radius of the fourth orbit of hydrogen atom is 0.85 nm. Calculate the velocity of electron in this orbit.
(

Q.25 The velocity of e− in a certain Bohr orbit of the hydrogen atom bears the ratio 1:275 to the velocity of AL,
P
light. What is the quantum no. "n" of the orbit and the wave no. of the radiation emitted for the transition O
m H
o from the quatum state (n+1) to the ground state. B
ses.cQ.26 Electrons of energy 12.09 eV can excite hydrogen atoms. To which orbit is the electron in the hydrogen 81 ,
s atom raised and what are the wavelengths of the radiations emitted as it drops back to the ground state. 8
a 8
l 5
ocQ.27 A doubly ionised lithium atom is hydrogen like with atomic number z = 3. Find the wavelength of the 0
k 3
e radiation required to excite the electron in Li2+ from the first to the third Bohr orbit. 9
t 8
ww.Q.28 Estimate the difference in energy between I and II Bohr Orbit for a hydrogen atom. At what minimum at 0 9
w no. a transition from n=2 to n=1 energy level would result in the emission of X−rays with 0,
: λ = 3.0 × 10−8 m? Which hydrogen like species does this at no correspond to. 00
e 0
bsitQ.29 Find out the no. of waves made by a Bohr electron in one complete revolution in its 3rd orbit. 2 0
e 3
w )-
m Q.30 Iodine molecule dissociates into atoms after absorbing light of 4500A0. If one quantum of radiation is 55
7
o absorbed by each molecule, calculate the K.E. of iodine atoms 0
r (
e f (Bond energy of I2 = 240 KJ/mol) H:
g P
kaQ.31 Calculate the wavelength of radiation emitted, producing a line in Lyman series, when an electron falls r)
c Si
Pa from fourth stationary state in hydrogen atom. K.
y Q.32 Calculate the wave no. for the shortest wavelength transition in the Balmer series of atomic hydrogen. R.
ud S.
St GENERAL A (
d Y
oaQ.33 What is de-Broglie wavelength of a He-atom in a container at room temperature.(Use U ) RI
l avg A
n K
owQ.34 Through what potential difference must an electron pass to have a wavelength of 500 Å. R.
DQ.35 A proton is accelerated to one- tenth of the velocity of light. If its velocity can be measured with a G
A
E H
E precision + 1%. What must be its uncertainity in position. U
R S
FQ.36 To what effective potential a proton beam be subjected to give its protons a wavelength of 1 ×10−10 m. r :
o
Q.37 Calculate magnitude of angular momentum of an e– that occupies 1s, 2s , 2p , 3d , 3p. ct
e
r
Q.38 Calculate the number of exchange pairs of electrons present in configuration of Cu according to Aufbau Di
Principle considering 3d & 4s orbitals. S,
E
Q.39 He atom can be excited to 1s1 2p1 by λ = 58.44 nm. If lowest excited state for He lies 4857cm–1 below S
S
the above. Calculate the energy for the lower excitation state. A
L
C
Q.40 Wave functions of electrons in atoms & molecules are called________. O
K
Q.41 The outermost electronic conf. of Cr is___________. E
T
EXERCISE-II e
r
u
t
c
Q.1 X-rays emitted from a copper target and a molybdenum target are found to contain a line of wavelengthu
r
2( 2Z. 8=5 4 n2m) ahtatrvieb uwteadv teole tnheg tKhα 1 l5in.e4 2of n amn i amnpdu 7ri.t1y2 e lnemme rnets. pTehcet iKveα llyin. eUs soifn cgo Mppoesr e (lZey =’s 2 l9a)w a,n γd1 m/2 o=l yab (dZe n–u bm)mic st
o
calculate the atomic number of the impurity element. At
0
2
of
Q.2 1.8 g hydrogen atoms are excited to radiations. The study of spectra indicates that 27% of the atoms are9
e
in 3rd energy level and 15% of atoms in 2nd energy level and the rest in ground state. If I.P. of H isg
a
P
21.7 × 10−12 erg. Calculate −
(i) No. of atoms present in III & II energy level. )
P.
(ii) Total energy evolved when all the atoms return to ground state. M.
(

L,
Q.3 One mole He+ ions are excited. Spectral analysis showed existence of 50% ions in 3rd orbit, 25% in 2nd A
P
and rest in ground state. Calculate total energy evolved when all the ions return to the ground state. O
m H
o B
ses.cQ.4 The energy of an excited H-atom is –3.4 eV. Calculate angular momentum of e–. 81 ,
s 8
a 8
oclQ.5 The vapours of Hg absorb some electrons accelerated by a potential diff. of 4.5 volt as a result of which 0 5
k light is emitted. If the full energy of single incident e− is supposed to be converted into light emitted by 3
e 9
ww.t single Hg atom, find the wave no. of the light. 0 98
wQ.6 The hydrogen atom in the ground state is excited by means of monochromatic radiation of wavelength 0,
0
: x A0. The resulting spectrum consists of 15 different lines . Calculate the value of x. 0
e 0
it 0
bs 2
eQ.7 The eyes of certain member of the reptile family pass a single visual signal to the brain when the visual 3
m w receptors are struck by photons of wavelength 850 nm . If a total energy of 3.15 × 10 −14 J is required 55)-
o to trip the signal, what is the minimum number of photons that must strike the receptor. 07
r (
e f H:
gQ.8 If the average life time of an excited state of H atom is of order 10–8 sec, estimate how many orbits an e– P
cka makes when it is in the state n = 2 and before it suffers a transition to n =1 state. Sir)
Pa K.
y Q.9 Calculate the frequency of e– in the first Bohr orbit in a H-atom. R.
ud S.
StQ.10 A single electron orbits around a stationary nucleus o f charge +Ze where Z is a constant from the A (
d Y
a nucleus and e is the magnitude of the electric charge. The hydrogen like species required 47.2 eV to RI
o
A
nl excite the electron from the second Bohr orbit to the third Bohr orbit. Find K
ow(i) the value of Z and give the hydrogen like species formed. R.
D G
(ii) the kinetic energy and potential energy of the electron in the first Bohr orbit.
A
E H
E U
FRQ.11 Alib setraattieodn aa pryh oHtoen+ eiolenc termonit ftreodm a ap shtoattioonn acroyr Hre saptoomnd inin ggr otou nad f sirtastte l.i nWe hoaft tihs eth Ley vmelaonc istye roife ps.h Tothoee plehcotrtoonn. or : S
t
c
e
r
Q.12 To what series does the spectral lines of atomic hydrogen belong if its wave number is equal to the Di
difference between the wave numbers of the following two lines of the Balmer series 486.1 and 410.2 nm. S,
E
What is the wavelength of this. S
S
A
L
C
O
K
E
T
Q.13 A particle of charge equal to that of an electron and mass 208 times the mass of the electron moves in ae
r
u
circular orbit around a nucleus of charge +3e. Assuming that the Bohr model of the atom is applicable to thisct
u
system, (a) derive an expression for the radius of the nth bohr orbit, (b) find the value of n for which the radiustr
of the orbit is approximately the same as that of the first Bohr orbit for th ehydrogen atom, and (c) find themic s
wavelength of the radiation emitted when the revolving particle jumps from the third orbit to the first. to
A
0
2
Q.14 A neutrons breaks into a proton and an electron. This decay of neutron is accompanied by release of energy.of
0
Assuming that 50% of the energy is produced in the form of electromagentic radiation, what will be the frequency1
e
g
of radiation produced. Will this photon be sufficient to cause ionization of Aluminium. In case it is able to do soa
P
what will be the energy of the electron ejected from the Aluminium atom. IE = of Al = 577 KJ/mol
1
)
P.
M.
Q.15 Find the number of photons of radiation of frequency 5 × 1013 s–1 that must be absorbed in order to melt
(

one gm ice when the latent heat of fusion of ice is 330 J/g. L,
A
P
O
mQ.16 The dye acriflavine, when dissolved in water, has its maximum light absorption at 4530 Å and its maximum H
o B
ses.c nfluumorbeesrc oenf cqeu aenmtais asibosno rabt e5d0.8 U0s Åin.g T thhee wnuamvebleern ogfth fslu oofr mesacxeinmcuem q uaabnstoar pist,i oonn athnde aevmeirsasgioen, ,5 w3%ha to %f t hoef 81 ,
as absorbed energy is emitted as fluorescence? 88
l 5
oc 0
k 3
eQ.17 Hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength 975Å. How 9
t 8
ww. many different lines are possible in the resulting spectrum? Calculate the longest wavelength amongst them. 0 9
wQ.18 An alpha particle after passing through a potential difference of 2 × 106 volt falls on a silver foil. The 00,
: 0
e atomic number of silver is 47. Calculate (i) the K.E. of the alpha-particle at the time of falling on the foil. 0
bsit (ii) K.E. of the α – particle at a distance of 5 × 10–14m from the nucleus, (iii) the shortest distance from 2 0
we the nucleus of silver to which the α−particle reaches. )- 3
m 55
ke2 7
roQ.19 Suppose the potential energy between electron and proton at a distance r is given by − . Use (0
e f 3r3 H:
g P
ka Bohr’s theory to obtain energy of such a hypothetical atom. r)
c Si
PaQ.20 An energy of 68 eV is required to excite a hydrogen like atom from its second Bohr orbit to the third. K.
udy The nuclear charge is Ze. Find the value of Z, the kinetic energy of the electron in the first Bohr orbit and S. R.
St the wavelength of the radiation required to eject the electrons from the first Bohr orbit to infinity. A (
d Y
oaQ.21 A proton captures a free electron whose K.E. is zero & forms a hydrogen atom of lowest energy-level RI
A
l
n (n = 1). If a photon is emitted in this process, what will be the wavelength of radiation? In which region K
ow of electromagnetic spectrum, will this radiation fall? (Ionisation potential of hydrogen = 13.6 volt, R.
D G
h = 6.6 × 10–34K/s, C = 3.0 × 108 m/s) A
E H
E U
R S
FQ.22 The ionisation energy of the hydrogen atom is given to be 13.6 eV. A photon falls on a hydrogen atom r :
which is initially in the ground state and excites it to the (n = 4)state. to
c
(a) show this transition in the energy-level diagram & e
r
(b) calculate the wavelength of the photon. Di
S,
E
S
Q.23 Calculate Total spin and the multiplicity for each possible configuration of N-atom. S
A
(A) (B) L
C
(C) (D) O
K
E
T