This document solves a physics problem to determine the accelerating voltage required to observe a second-order beam at an angle of 55° in the Davisson-Germer experiment using a Ni crystal. It uses the Bragg diffraction equation and de Broglie wavelength equation to relate the nickel crystal spacing of 0.215 nm to an electron wavelength corresponding to an acceleration voltage of 193.83 keV.

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

2. 2
No.2
No.3

3. 3
No.4

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
 = +
 = 