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A free electron has kinetic energy
K
=
1
K = 1
K
=
1
eV
=
1.60218
e
−
19
= 1.60218e-19
=
1.60218
e
−
19
J. Its momentum is
p
=
2
⋅
m
⋅
K
p = \sqrt{2 \cdot m \cdot K}
p
=
2
⋅
m
⋅
K
and the matter wavenumber is
k
=
p
/
ℏ
k = p/\hbar
k
=
p
/ℏ
. Using
m
=
9.10938
e
−
31
m = 9.10938e-31
m
=
9.10938
e
−
31
kg and
ℏ
=
1.05457
e
−
34
\hbar = 1.05457e-34
ℏ
=
1.05457
e
−
34
J
⋅
\cdot
⋅
s, what is
k
k
k
in
m
−
1
m^{-1}
m
−
1
?
≈ 5.40e-34
m
−
1
m^{-1}
m
−
1
≈ 7.24e9
m
−
1
m^{-1}
m
−
1
≈ 2.56e9
m
−
1
m^{-1}
m
−
1
≈ 5.12e9
m
−
1
m^{-1}
m
−
1
Check answer