
70%1)-%.30170%1)-%.301/#%$41/#%$41%%
$*4235$*4235/,3!'%2!.$#411/,3!'%2!.$#411%.3%.3
#=B3#=B3 34=@3AE7B167<5=<B63>=E3@03AC@3B6/B/::>=E3@
AE7B163A=<B63%=E3@(C>>:73A/@37<B63$>=A7B7=</<2/::
D=:B/531=<B@=:A/@3BC@<324C::G1=C<B3@1:=19E7A3
$<B63)C</0:3=<AB/<B+=:B/53%=E3@(C>>:GA3BB63
+=:B/53'/<53(E7B16B= K+K+
=@0=B6>=E3@AC>>:73A>CA67<B63%=E3@(E7B16B=B63$#
>=A7B7=<
::=EB63P:/;3<BB=63/BC>4=@/0=CB;7<CB3A
$<B63)C</0:3=<AB/<B+=:B/53%=E3@(C>>:GA3BB63
113:3@/B7<5+=:B/53B=+
=<<31B/E7@303BE33<B63 113:3@/B7<5+=:B/53113:3@/B7<5+=:B/53
>=A7B7D3
B3@;7</:B=B63 3Q31B7=<%:/B3A3Q31B7=<%:/B3A
*>>3@
B3@;7</:B=;/93B63
3:31B@=<03/;/>>3/@
$<B63)C</0:3=<AB/<BC@@3<B%=E3@(C>>:G7<1@3/A3B63
1C@@3<BB=B633:;6=:BH1=7:A,/B16B633:31B@=<03/;/<2
16319B6/BB633:31B@=<03/;1C@D3AC>E/@2=<B7<C37<1@3/A7<5
B631C@@3<BC<B7:B633:31B@=<03/;4=@;A/1:=A3217@1:3
◦4B633:31B@=<03/;2=3A<=B23Q31B@3D3@A3B63>=:/@7BG=4
=<3=4B633:;6=:BH1=7:AA=B6/B1C@@3<B>/AA3AB6@=C560=B6
1=7:A7<B63A/;327@31B7=<
◦4B633:31B@=<03/;23Q31BA2=E<E/@2AE/>B631=<<31B7=<A
=<B63=CB>CBB3@;7</:A=<B63%=E3@(C>>:G
◦4B633:31B@=<03/;4=@;A/A>7@/:@=B/B3B63BC03=<B63
>:/B4=@;C<B7:/1:=A3217@1:37A4=@;32.=C;/G/:A=<332B=
@=B/B3B63>:/B4=@;B=B63@756B=@:34BB=/:75<B63;/5<3B71
P3:253<3@/B320GB633:;6=:BH1=7:AE7B6B63;/5<3B71P3:2
=4/@B6
7A1=<<31BB63E7@303BE33< 113:3@/B7<5+=:B/53113:3@/B7<5+=:B/53
>=A7B7D3
B3@;7</:B=B63 3Q31B7=<%:/B3A3Q31B7=<%:/B3A
*>>3@
B3@;7</:
$<%=E3@(C>>:G/28CABB63D=:B/53=CB>CBB=B63113:3@/B7<5
+=:B/53B==>B7;7H3B634=1CA/<20@756B<3AA=4B633:31B@=<
03/;
%#/1%#/1$$!3!$$!3!
'3/2B631C@@3<B27A>:/GB=P<2B631C@@3<B
B6@=C56B63
3:;6=:BH1=7:A'31=@2B63D/:C37<)/0:3
'3/2B63D=:B;3B3@/<2@31=@2B63113:3@/B7=<+=:B/53
*
7<)/0:3
"3/AC@3B63@/27CA
@
=4B633:31B@=<03/;!==9B6@=C56B633;
BC03/BB63;7@@=@32A1/:3)=/D=72>/@/::/F3@@=@A;=D3G=C@
63/2B=/:75<B633:31B@=<03/;7<B63BC03E7B6B63@3Q31B7=<=4
B6303/;/AG=CA337B7<B63;7@@=@32A1/:3"3/AC@3B63@/27CA
=4B633:31B@=<03/;/AG=CA337B=<0=B6A723A=4B63A1/:3/<2
/D3@/53B63@3AC:BA'31=@2B63/D3@/53@/27CA7<)/0:3
=::31B/227B7=</:B@7/:A=42/B/CA7<527O3@3<B/113:3@/B7<5
D=:B/53A/<21C@@3<BB6@=C56B633:;6=:BH1=7:A
#=B3#=B3 4G=C:=A3B633:31B@=<03/;E67:3/28CAB7<5B63
/113:3@/B7<5D=:B/53@3>3/BAB3>A7<B63 28CABD=:B/53A/<228CABD=:B/53A/<2
1C@@3<B1C@@3<B >@=132C@3
.!,82)2/&%--%!241.!,82)2/&%--%!241%-%.32%-%.32
)63;/5<3B71P3:2
53<3@/B327</>/7@=43:;6=:BH1=7:A7A
>@=>=@B7=</:B=B631C@@3<B
>/AA7<5B6@=C56/A7<5:31=7:)63
1=<AB/<B=4>@=>=@B7=</:7BG
9
1/<0323B3@;7<324@=;B631=7:@/27CA
'
/<2B63<C;03@=4BC@<A
#
=<B631=7:
B=
(
4
5
)
3
2μoNIH
R
,7B6B67A3F>@3AA7=<4=@
B637<7B7/:4=@;C:/4=@3;
e
m=2U
B2r2
031=;3A
e
m= 2U
(
5
4
)
3R2
(
μoNIHr
)
2
'
;;
#
BC@<A>3@1=7:
μ= J
)63/113>B32D/:C3=4B6316/@53B=;/AA@/B7=
3;
7A
J 95
!",% !3!
%-/.231%-/.231!3)/.2!3)/.2
3Q31BB6303/;CA7<5/<3:31B@71P3:23Q31BB6303/;CA7<5/<3:31B@71P3:2
,7B6<=1C@@3<B7<B633:;6=:BH1=7:A23Q31BB6303/;CA7<5B63
23Q31B7=<>:/B3A
N =<<31B/E7@303BE33<B63 113:3@/B7<5+=:B/53113:3@/B7<5+=:B/53
>=A7B7D3
B3@;7</:
B=B63 3Q31B7=<%:/B3A3Q31B7=<%:/B3A
*>>3@
B3@;7</:B=;/93B633:31B@=<03/;
23Q31BC>E/@2A
N (E7B16B63E7@3B=B63 3Q31B7=<%:/B3A3Q31B7=<%:/B3A
!=E3@
B3@;7</:B=;/93
B633:31B@=<03/;23Q31B2=E<E/@2A
3Q31BB6303/;E7B6/>3@;/<3<B;/5<3B3Q31BB6303/;E7B6/>3@;/<3<B;/5<3B
=:2/>3@;/<3<B0/@;/5<3B<3/@B63BC03B=A6=EB633O31B=4/
;/5<3B71P3:2=<B633:31B@=<03/;(E7B1603BE33<6=:27<5B63
<=@B63<2/<2B63A=CB63<2=4B63;/5<3B<3/@B6303/;
'=B/B3B63BC03'=B/B3B63BC03
'=B/B3B63BC03A=B6/B7B7A=@73<B32/B/</<5:3E7B6@3A>31BB=B63
;/5<3B71P3:24@=;B633:;6=:BH1=7:AAG=C@=B/B3B63BC03
=0A3@D36=EB6303/;23Q31B7=<7A/O31B32
3Q31BB6303/;CA7<5/@B6A;/5<3B71P3:23Q31BB6303/;CA7<5/@B6A;/5<3B71P3:2
,7B6<=;/5<3B/<2<=1C@@3<B7<B633:;6=:BH1=7:A@=B/B3B63BC03
=@B633<B7@3/>>/@/BCAB=A33B6323Q31B7=<=4B6303/;2C3B=B63
/@B6MA;/5<3B71P3:2AB6327@31B7=<=4B6323Q31B7=<=4B6303/;/A
G=C3F>31B
4 | Electron Charge-to-Mass Ratio