1. 1
In the Davisson-
Germer experiment
using a Ni crystal, a
second-order beam
is observed at an
angle of 55◦
. For
what accelerating
voltage does this
occur?
HELPING TOOLS
No.1
4. 4
Solution
We know that maxima for a diffraction
grating occur at angles such that the
path difference between adjacent rays
sin is equal to a whole number of
wavelengths:
sin 1,2,3,... (1)
where is
d
d n n
n
= = − − − −
the order number of the
maximum.
From independent data, it is known
that the spacing between the rows of
atoms in a nickel crystal is
0.215 .
d nm
=
5. 5
Using
2, 55 , 0.215
in eq.(1), we get
0.215n sin 55 2
0.215n sin 55
2
0.215 0.82
2
0.08815
n d nm
mX
mX
nmX
nm
= = =
=
=
=
=
8
15
9
2
,
2.998 10
4.136 10 .
0.0881 10
140.746 10
14074.6
Also
E hf h h
p p
c c
m
X
X eV s s
p X
X m c
eV
p X
c
eV
p
c
−
−
= = = =
=
=
=
6. 6
2
2
2
2
2
2
,
1
K &
2 2
(14074.6 )
2
198094365.16( )
2
198094365.16( )
2 511000
193.83
Now
p
mv p mv K
m
eV
c
K
m
eV
K
mc
eV
K
X eV
K eV
= = =
=
=
=
=
This desired KE, i.e. 193.83
must be achieved & for achieving
this one, the electrons must be accelerated
through a PD of 193.83 as
electric PE & potential are related by
eV
V V
U q V
= +
=
