physics formula sheet2

8/12/2019 Physics Formula Sheet2

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Grade 12

Formula Sheet

Unit: Atoms and Nuclei

1. Rutherford's particle scattering

(a) N() cosec4 (/2)

(b) Impact parameter, b= Ze2 cot/2

40 E, (whereE=

1

2mu

2=KE of the ! part"c#e)

2. Distance of closest approach:

r0= 2 Ze

2

40 E, (where E=

1

2mu

2=KE of the ! part"c#e)

3. Bohr's atomic model

(a) $=m%r=&h2'

(b) h%=Ei=E f=hc

(c) ad"us of &th orb"t

r&&

2

Z, r&=

&2

Z h2

42m *e

2 (d) +e#oc"t of e#ectro& "& &th orb"t

%

&=

Z

&

c

1-.

=

Z

& c

(where

=

2' Ke2

c h =

1

1-. f"&e structures co&sta&t)

4. Total energ of electron:

(a) ote&t"a# e&er, ! (*Ze2/r)

(b)K"&et"c e&er, K=1

2m%

2= *Ze 2/2 r


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(c) 3ota# e&er, E K ! (*Ze2/2r) (/2) ! K

(d) K ! (/2) or 2K 2E

(e) E&=1-56Z2

&2

e+=Z2

&2

2'2 m *2 e4

h2 =

25178 1017 Z2

&2

9

(f) :er"es formu#a (wa%e &umber %=1/

1

= (Z2 1n12

1

n22 were (=2'

2m *

2e

4

c h- =150;.10

.m

1

() :er"es formu#a for < ! atom

(") $ma& ser"es

1

=

(

1

1

&2 ,&

=2,-, 4,55555555

("") =a#mer ser"es 1

=(122

1

&2 ,&=-,4,>,55555555

(""") asche& ser"es 1

=(1-2

1

&2 ,&=4,>,6,55555555

("%) =rac*et ser"es 1

=(142

1

&2 ,&=>,6,.,55555555

(%) ! fu&d ser"es 1

=(1>2

1

&2 ,&=6,.,7, 55555555

!. "um#er of emission lines from e$cited state:

& &(& ! 1)/2

%. Time period of re&olution:

3& (&-/Z2)

. (re)uenc of re&olution:

%& (Z2/&-)

*. +urrent due to or#ital motion:

I& (Z2/&-)

,. -agnetic field at nucleus due to or#ital motion of electron


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=& (Z-/&>)

1. -agnetic moment:

(a) ?& (e$/2m) (&he/4'm)@

(b) ?1 (eh/4'm) A= =ohr ?a&eto& ;52. B 10!24Cm2

11. -agnitude of angular momentum :

$ D ( 1) F (h/2')

12. /ngle of angular momentum &ector from 0 a$is

(a) cos mlD ( 1)HF

(b) the #east ae "s for m "5e5 cos m"& /D ( 1)H F

13. -agnitude of spin angular momentum

:= [s s1] h /2'= -

2 h /2'


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R/

1. +ontinuous ras:

(a) %ma8 (e+/h)

(b) m"& (hc/e+) (12400/+)

2. +haracterictic ras :

(a) KJ $J ?

(b) +K +$ +?

3. (re)uenc of line:

% K=- c(

4 Z12=254.101> Z12

4. 5a&elength of line:

(K) 4/-(Z!1)2F 1216/(Z ! 1)2F

!. 6nerg of 7ra photon:

E(K) 1052 (Z!1)2e+

%. -osle's la8:

(a) % a (Z!b)2, were a (-c/4) 254. B 10>


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-/TT6R 5/;6

1. (or photons:

(a) E h% (hc/)@

(b) p (h%/c) (E/c) (h/)@

(c) m (E/c2) (h%/c2) h/c

(d) rest mass 0, chare 0, sp"& 1 (h/2 ')

2. -atter 8a&es:

(a) de =ro#"e wa%e#e&th, =

h

p=

h

m%=

h

2 mE =

h

2 m +[E=

1

2m%

2

=+ ](") Mor e#ectro& e=

1252.

+C

("") Mor proto& p=05276

+C

(""") Mor a#pha part"c#e =05101

+C

(b) Mor part"c#e at temperature 3 = h-m K3

E= -2

*3

(c) 3he wa%e#e&th of e#ectro& acce#erated b pote&t"a# d"ffere&ce of + %o#ts "s e=

1252.

+C

(d) Oo&d"t"o& for obta"&"& stab#e orb"t 2 'r& &

(e) 3he phase %e#oc"t of a de =ro#"e wa%e of wa%e#e&th a&d freue&c % "s

%p=% =E

h

h

m%=

mc2

h

h

m%=

c2

%"5e5 %pc

(f) Group %e#oc"t, % (d/d*)5 It "s fou&d that roup %e#oc"t "s eua# to part"c#e %e#oc"t "5e5,% %


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R/D


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Grade 12

(c) N=6502- 10

2-m

C

%. Radioacti&e e)uili#rium:

NCC N==

. Deca constant for t8o channels:

(a) =1 2@

(b)3= 31 32

3132

*. >amma


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Grade 12

"?+@6/R A9 ?e+

2. Aroperties of nucleus:

(a) ad"us 0C1/- where 0152 ferm"

(b) +o#ume+C[+=4- (-= 4- (0- C ](c) Qe&s"t 254 B 101.K/m-("s "&depe&de&t of C)

3. -ass defect:

R ?Zmp (C!Z) m&! ?

4. Aacing fraction:

f R/C mass e8cess per &uc#eo& R ! R? mass e8cessF

!. Binding energ:

E =E (R?)c2

physics formula sheet2

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