8. Uncertainty in the position of an electron
(mass = 9.1 x 10-31 kg) moving with a velocity
300ms accurate upto 0.001% will be
h = 6.63 x 10-34Js)
1) 3.84 x 10-2 m 2) 19.2 x 10-2 m
3) 5.76 x 10-2 m 4) 1.92 x 10-2 m
Answers
Answer:
UNCERTAINTY IN POSITION - VELOCITY - MOMENTUM
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Uncertainty in the position of an electron (mass = 9.1 x 10-34 kg) moving with a velocity 300 m s-1 , accurate up to 0.001%, will be: (h= 6.63 x 10-34 J s)
(AIEEE 2006)
a) 19.2 x 10-2 m
b) 5.76 x 10-2 m
c) 1.92 x 10-2 m
d) 3.84 x 10-2 m
Logic:
According to Heisenberg's uncertainty principle, the product of uncertainties in position (Δx) and velocity (Δv) is always equal to or greater than h/nπ.
i.e.
What is the meaning of "accurate up to 0.001%"?
It indicates that the uncertainty in velocity is 0.001% of actual value, 300 m s-1.
i.e.
uncertainty in velocity (Δv) = 300 x 0.001 / 100 = 3 x 10-3 m s-1
Solution:
The uncertainty in position (Δx) can be calculated as follows:
Note: n = 4 for electron.
Conclusion:
The correct option is "c".
Related questions
1) If the uncertainties in velocities of two particles A and B with mass 1.0 x 10-27 kg and 1.0 x 10-31 kg respectively are same, the ratio of uncertainties in the positions of A and B is:
(EAMCET 2011-E)
a) 1000 :1
b) 10,000:1
c) 1: 1000
d) 1:10,000
Logic & solution:
The uncertainty in position, Δx is given by the expression:
The ratio of uncertainties in positions for A and B is:
Note: h/nπ is constant and Δv values are same.
Conclusion:
Correct option is "c".
2) The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 m s-1 respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties?
(EAMCET 2006-E)
a) 2
b) 0.25
c) 4
d) 1
Logic & solution:
The uncertainty in position, Δx is given by the expression:
The ratio of uncertainties in positions for A and B is:
Note: mB = 5mA
Conclusion:
Correct option is "a".
3) Uncertainty in position of a particle of 25 g in space is 10-5 m. Hence, uncertainty in velocity (m s-1) is: ( Planck’s constant, h = 6.6 x 10-34 J s)
(AIEEE 2002)
a) 2.1 x 10-28
b) 2.1 x 10-34
c) 0.5 x 10-34
d) 5.0 x 10-24
Logic & solution:
The uncertainty in velocity, Δv is given by the expression:
Conclusion:
Correct option is "a".
4) In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainty with which the position of the electron can be located is: (h=6.6 x 10-34 kg m2 s-1; mass of electron, em = 9.1 x 10-31 kg )
(AIEEE 2009)
1) 1.52 x 10-4 m
2) 5.10 x 10-3 m
3) 1.92 x 10-3 m
4) 3.84 x 10-3 m
Logic & solution:
Since the accuracy in velocity is 0.005%, uncertainty in velocity, Δv = 600 x 0.005 / 100 = 3 x 10-2 m s-1.
Uncertainty in position will be:
Conclusion:
Correct option is "3".
Homework
1) State Heisenberg's uncertainty principle.
2) What will be the uncertainty in momentum of electron if the uncertainty in its position is zero?
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