YouTube Lecture # 18

1. 1
Find the potential difference through which
electrons must
be accelerated (as in an electron microscope,
for example) if we wish to resolve: (a) a virus
of diameter 12 nm; (b) an atom of diameter
0.12 nm; (c) a proton of diameter 1.2 fm.

2. 2
Helping Tools
No.1

3. 3
No.2

4. 4
No.3

5. 5
No.4

6. 6
No.5

7. 7
Solution
(a)

8. 8
15
9
8
15
9
7 2
9
( ) A virus of diameter 12 nm
4.136 10 .
12 10
2.998 10
4.136 10 .
12 10
12.40 10 1.033 10
103.3
12 10
a
h X eV s
p
X m
m
X
X eV s s
X
X m c
X eV X eV eV
X c c c

−
−
−
−
−
−
= =
=
= = =

9. 9
2
2
2
2
2
2
2
2
,
(103.3 )
1
K &
2 2 2
( )
10670.89
10670.89( )
2 2
10670.89( ) 10670.89( )
2 511000 1022000
0.01
Also
eV
p c
mv p mv K
m m
eV
eV
c
m mc
eV eV
X eV
eV
= =  = =
= =
= =
=

10. 10
,
0.01
0.01V
. must decrease to increase K.E
Now
U eV
U q V V
q e
P E
 −
 =    = = = +
−

11. 11
(b)
15
9
8
15
11
5 4
9
( ) An atom of diameter 0.12 nm
4.136 10 .
0.12 10
2.998 10
4.136 10 .
12 10
12.40 10 1.033 10
10330
12 10
b
h X eV s
p
X m
m
X
X eV s s
X
X m c
X eV X eV eV
X c c c

−
−
−
−
−
−
= =
=
= = =

12. 12
2
2
2
2
2
2
2
2
,
(10330 )
1
K &
2 2 2
( )
106708900
106708900( )
2 2
106708900( ) 106708900( )
2 511000 1022000
104.4
Also
eV
p c
mv p mv K
m m
eV
eV
c
m mc
eV eV
X eV
eV
= =  = =
= =
= =
=

13. 13
,
104.4
104.4V
. must decrease to increase K.E
Now
U eV
U q V V
q e
P E
 −
 =    = = = +
−

14. 14
(c)
15
15
8
8 9
( ) A proton of diameter 1.2 fm
4.136 10 .
1.2 10
2.998 10
3.45 .
10.34 10 1.034 10
1034
c
h X eV s
p
X m
m
X
eV s s
X
m c
X eV X eV MeV
c c c

−
−
= =
=
= = =

15. 15
9 2
2
2
2
18
18 2
2
2
18 2 18
12
12
,
(1.034 10 )
1
K &
2 2 2
( )
1.069 10
1.069 10 ( )
2 2
1.069 10 ( ) 1.069 10 ( )
2 511000 1022000
1069000 10
1.045988 10
1022000
Also
eV
X
p c
mv p mv K
m m
eV
X
X eV
c
m mc
X eV X eV
X eV
X eV eV
X
c c
= =  = =
= =
= =
= =

16. 16
12 8
0
2 2 2
10 10
,
( ) ( )
E K E K
Similarly
E pc mc E pc
 = + 
= +  

17. 17
,
1034 1034
Hence
MeV
K E pc Xc MeV
c
  = =

18. 18
9
,
1034
1034MV=+1034000000V
=+1.034X10 V
. must decrease to increase K.E
Now
U MeV
U q V V
q e
P E
 −
 =    = =
−
= +
The End