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Byju's Answer
Standard XII
Chemistry
Heisenberg's Uncertainty Principle
The minimum u...
Question
The minimum uncertainty in the speed of an electron in a one dimensional region of length
2
a
0
(where
a
0
=
Bohar radius
52.9
pm) is
k
m
s
−
1
.
(Given : Mass of electron
=
9.1
×
10
−
31
kg, Planck's constant
h
=
6.63
×
10
−
34
J
s
)
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Solution
Heisenberg's uncertainty principle
Δ
x
×
Δ
P
x
≥
h
4
π
⇒
2
a
0
×
m
Δ
v
x
=
h
4
π
(minimum)
⇒
Δ
V
x
=
h
4
π
×
1
2
a
0
×
1
m
=
6.63
×
10
−
34
4
×
3.14
×
2
×
52.9
×
10
−
12
×
9.1
×
10
−
31
=
548273
m
s
−
1
=
548.273
k
m
s
−
1
=
548
k
m
s
−
1
Suggest Corrections
52
Similar questions
Q.
Uncertainty in the position of an electron
(
m
a
s
s
=
9.1
×
10
−
31
k
g
)
moving with a velocity
300
m
s
−
1
accurate upon 0.001% will be:
[
h
=
6.63
×
10
−
34
J
−
s
]
Q.
Determine uncertainty in the position of an electron moving with a velocity 300 m. sec
−
1
accurate up to 0.001 %
[
h
=
6.63
×
10
−
34
J.s and mass of electron
=
9.1
×
10
−
31
kg]
Q.
An accelerated electron has a speed of
5
×
10
6
m
s
−
1
with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is
x
×
10
−
9
m
. The value of x is
.
[Use mass of electron
=
9.1
×
10
−
31
k
g
,
h
=
6.63
×
10
−
34
J
s
,
π
3.14
]
Q.
If an electron is moving with velocity
500
m
s
−
1
, which is accurate up to 0.005% then calculate uncertainty in its position. [
h
=
6.63
×
10
−
34
J
−
s
,
m
a
s
s
o
f
e
l
e
c
t
r
o
n
=
9.1
×
10
−
31
K
g
]
Q.
If the mass of electron is
9.11
×
10
−
31
kg. Planck's constant is
6.626
×
10
−
34
J-s and uncertainty in position is
0.1
o
A
, then uncertainty in velocity is?
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