




Milan Raspopovi}
Branislav Cvetkovi}
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Milan Raspopovi}
Branislav Cvetkovi}



S (x,y,z,t) (x’,y’,z’,t’) T
x=x’+ut ut x x’
S (x, y, z
S’ (x’, y’, z’
t = t’ t ut
S : x = x’ + ut; y = y’; z = z’ t = t’; S’ x’ = x – ut; y’ = y ; z’ = z t’ = t. x v S v = x t , S’ v’ = , x t .
t = t’ x = x2 – x1
x = x’ + u t t
t x = , x t + u,
v = v’ + u.
v = v ’ + u
8 m s
v x = v x ’ + u v y = v y ’, vz =v z ’ v x ’ = c
x ’













8 kg? c = 2, 9979 · 108 , m e = 9,1095 · 10–31 kg; E0 =
E0,e = m e c2 = 9,1095 · 10–31 kg (2,9979 · 108 ms–1)2, E0,e = 8,187 · 10–14 J




c 8 m s
t t
v t t v u v’ v 2 1 , , vu uv c v’ 2 1 vu uv c
v’ S’ v S u S’ S c 2 , vu c v’ u
v = v’ ± u p 2 2 1 m v c v
E0 = mc2 v
E2 – c2p2 = (mc2)2
E2 – c2p2 = const, mc2 2 2 2 – 1 c E v = mc



i
ν h ν = Ejon + Ai + Ek
jon
eV J)
k v << c Ek = 1 2 m e v2
ν0 = Ai ν0 = iA h

v 2 i hc A m λ v 5 m s m nm kg λ m λ m Ai Ek λ i hc A
Ai J h ν Ai 2 1 m v ν c λ
v 2 i hc A m λ v 5 m s .
Ek 2 1 mv 19 J m V
λ m U z V Ai
h ν 34 8 7 66210310 10 m ,Js s m J eV
h ν 2 1 m v eU z
Ai h ν eU z eV eV
Ai eV hc

λ = h mv = m m m
eU = E = Ek – Ek0 = Ek = 1 2 m e v2 , v E v = 2 e eU m λ = e h mv = : h = 6,626 · 10 34 Js, e = 1,6 · 10 19 C m e = 9,1 · 10 31 kg U = 100 V, λ = 1,23 · 10 10 m = 0,123 nm. V nm m 2 e h emU 34 2 66210 510662 Js m kg s , Js kg s m










3646 Å 4110 Å4340 Å4861 Å6562Å
4000 Å
5000 Å6000 Å
m = 1 1 λ = R 22 11 2 n , n = 2, 3, 4,...,
m = 1 1 = R 22 11 1 n , n = 2, 3, 4,...,
m = 2 1 λ = R 22 11 2 n , n = 3, 4, 5,...,
m = 3 1 λ = R 22 11 2 n , n = 4, 5, 6,...,
m = 2 1 = R 22 11 2 n , n = 3, 4, 5,..., m = 3 1 = R 22 11 3 n , n = 4, 5, 6,...,
m = 4 1 λ = R 22 11 2 n , n = 5, 6, 7,..., m = 5
λ = R 22 11 2 n n МОДЕЛИ АТОМА
λ = R 22 11 2 n , n = 6, 7, 8,..., m = 6
m = 4 1 = R 22 11 4 n , n = 5, 6, 7,..., m = 5 1 = R 22 11 5 n , n = 6, 7, 8,..., m = 6 1 = R 22 11 6 n , n

L n = m v n r n = 2 nh π = n n = 1, 2, 3,..., m v r n
h (h = 6,626 · 10–34 Js).
h ν nm = E nm = E n – E m n m n
π r n
n λ= 2 π r n n = 1, 2, 3,..
r n λ
n = 2
λ = en h mv
L n = m e r n v n = n = n
n = 3
n = 4 2 h
n = 1
n = 2, 3 h, e, Z m E n E m n > m
h ν nm = E n – E m = 24 22 0 8 e mZe h ε 22 11 mn m m n ν nm = 069 , λ e λ = 24 22 0 8 e mZe h ε 22 11 mn , –n = 7 n = 6 n = 5 n = 4 n = 3 n = 2 n = 1
nm = nm c nm hc = 24 22 0 8 e mZe h 22 11 mn ,
serija
kg C
: U = 100 V, m e = 9,1 · 10–31 kg; e = 1,6 · 10–19 C; λ = ?
Ek = eU = 100 eV = 100 · 1,6 · 10–19 J = 160 · 10–19 J, keV
Ek = 2 1 m e v2 = 2 2 e p m , p = 2 ekmE
λ dN dt 2 ek h mE
v 2 k e E m , λ= 2 k e e h E m m = 2 ek h mE , λ = m h p 2 ek h mE 1,2 10–10 m
keV
: m e = 9,1 · 10–31 kg, Ek= 0,5 keV = 0,8 · 10–16 J, h = 6,62 · 10–34 Js; λ = ? λ h mv Ek = 2 1 mv2
m
2r = 10–10 m; Ek = ?
x 2 r 0,5 ·10–10 m
v h mx
Ek = 2 1 mv2 2 1 m v2;
Ek 2 2 2 h mx ; Ek 9,6 · 10–17 J = eV
9,1 · 10–31 kg e = 1,6 · 10–19 C
ε0 = 8,85 · 10–12 m s
r1 = ? v1 = ?; r2 = ? v2 = ?
1 = ? v1 2 = ? v2 = ? 2π nh πm e e ε0n2h2
r n = 22 22 4 0e n h me πε , n = 1, 2, 3,... ,
v n = 2 0 n e h ε
r1 = –m v1 = 6 m s,
r2 = –m v2 6 m s 0 = 8,85 · F m
F m ;
n = 1 n = 2, Z = 1, m e = 9,1 · 10–31 kg, e = 1,6 · 10–19 C ε0 8,85 · 10–12 m s ;
h ν E nm = E n E m n m λ = p h px x 2 h
L n = m v n r n = n 2 1 n = n
n E n E n E pn E n = E n + E pn = 22 0 8 n eZ r πε n E n 2 1 n 24 22 0 8 e mZe h ε E n 2 1 n J 2 1 n

s p d f g


n m s.
s, n m s = 2 1 .
n=4 M; n=3 L; n=2
K; n=1



p–n p –
p
p
p p- n p n pn p-
n p n n p n p n p
p n p n p n p n p n p n
pumpawe
spontana emisija izaziva prinudu ksenonska lampa (zra¦ewe za pumpawe)
ogledalo
svetlost =0,6943μm
reflektor kristal rubina 1-2% providno ogledalo
=0,6943μm laserovawe
=0,6943μm
ogledalo prinudna emisija supstanca lasera
spontana emisija pobuªeni atomi zra¦ewe za pumpawe
delimi¦no providno ogledalo


6 C 13 6 C
13 6 C 14 7 N
0,51,01,52,0 r(10–15 m)

4,0329 4,0026


jezgro
helijuma
elektron gama foton
jezgro roditeq (Z,A) pre raspada
alfa ¦estica
jezgro potomak (Z-2,A-4) posle raspada
alfa ¦estica gama
pre –-raspada posle
-raspada brzi elektron (beta zraæewe) gama zraæewe



ureðaj za brojawe impulsa
scintilatorska cev
pojaæavaæ
brojaæ impulsa
elektronski multiplikator
0,3 mSv
zraæewe iz kosmosa zraæewe iz tela
0,3 mSv
0,5 mSv zraæewe iz zemqišta
Q > Q <
D + D He + n
p + Li Be + n
γ + Be 2 He + n
n + S P + p
α + N 8O + p α + Be 6C + n
1. posuda reaktora
2. biološki štit ( obiæno beton)
3. nuklearno gorivo (235U, 238 U, 239 Pu)
4. moderator (teška voda, berilijum, grafit)
5. rashladno sredstvo (najæeš©e obiæna voda)
6. reflektor neutrona (berilijum, grafit)
7. kontrolne šipke (kadmijum, bor...)
8. sigurnosna šipka (apsorber neutrona)
kontrolne
reaktor primarna pumpa sekundarna pumpa kondenzator pare turbina generator generator pare

N
N = N0 t e , N t N0 t λ
2 ln T
, dN
N λ N
A = N + Z, N Z
E v mc2, m = Zm p + (A – Z) mn – M
r = r 0693 , λ , r m A 4 2 α + 9 4 Be + 1 0 n
2 1 D 1 0 n 4 2 α n 1 0 r = r0 3 A , 12 6 C
1 D + 31T 4 2 + n 1 0 .
up quark down quark
кварк strange quark
charmed quark
botton quark дно кварк top quark
p n + ν e n p – + n p –ν e π + n K– + K 0
E h ν h ν = E = 511 keV
λ = c ν = = m = 0 hc E = e h mc


=


100 000 svetlos. god.
spiralni kapci jezgro Sunce smer rotacije
zatvorena zvezdana jata
Pogled normalno na galakti¦ku ravan
10 000 sv. god.
Pogled na galakti¦ku ravan




Udaqenost od Sunca u milijardama kilometara











(1858–1947)


ВИЛХЕЛМ РЕНДГЕН ( 1845–1923)

РОБЕРТ ОПЕНХАЈМЕР (1904–1967)

( 1909–1994)

ISBN 978-86-17-20847-7
1.


