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Uncertainty in the position of an electron (mass 9.1 x 10-31 kg) moving with a velocity of 300 ms-1, accurate upto 0.001% will be:
- a)1.92 x 10-2 m
- b)3.84 x 10-2 m
- c)19.2 x 10-2 m
- d)5.76 x 10-2 m
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving...
Change in position (X),
P= momentum,
P=mv.
X ×P = h/4π.
X× m v = h/4π.
X= h/4πmv.
X=6.625×10-34/4 ×3.14×9.1×10^-31×300.
X=6.625×10-5/342.8.
X=0.0192×10^-5.
X= 19.2× 10-7.
in question it is given to take accurate up to 0.001%.= 1×10-3/100=1 ×10-5.
X= 19.2 ×10-7/10-5.
X=19.2 × 10-2.
P= momentum,
P=mv.
X ×P = h/4π.
X× m v = h/4π.
X= h/4πmv.
X=6.625×10-34/4 ×3.14×9.1×10^-31×300.
X=6.625×10-5/342.8.
X=0.0192×10^-5.
X= 19.2× 10-7.
in question it is given to take accurate up to 0.001%.= 1×10-3/100=1 ×10-5.
X= 19.2 ×10-7/10-5.
X=19.2 × 10-2.
Most Upvoted Answer
Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving...
**Given data:**
- Mass of the electron (m) = 9.1 x 10^-31 kg
- Velocity of the electron (v) = 300 m/s
- Accuracy = 0.001% = 0.00001
**Uncertainty principle:**
The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to simultaneously determine the exact position and momentum of a particle with absolute certainty.
Mathematically, the uncertainty principle can be expressed as:
Δx * Δp ≥ h/4π
where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck's constant.
**Calculating the uncertainty in momentum:**
The momentum of an electron can be calculated using the formula:
p = m * v
where p is the momentum, m is the mass, and v is the velocity.
Substituting the given values, we get:
p = (9.1 x 10^-31 kg) * (300 m/s)
p = 2.73 x 10^-28 kg m/s
**Calculating the uncertainty in position:**
Using the uncertainty principle equation, we can rearrange it to solve for Δx:
Δx = (h/4π) / Δp
Substituting the values, we get:
Δx = (6.626 x 10^-34 J s / (4π)) / (2.73 x 10^-28 kg m/s)
Δx = 7.63 x 10^-7 m
**Converting the uncertainty to a percentage:**
To convert the uncertainty to a percentage, we can use the formula:
Uncertainty percentage = (Δx / x) * 100
where Δx is the uncertainty and x is the position.
Substituting the values, we get:
Uncertainty percentage = (7.63 x 10^-7 m / x) * 100
Given that the uncertainty percentage is 0.001%, we can write it as 0.00001.
0.00001 = (7.63 x 10^-7 m / x) * 100
0.00001 = 7.63 x 10^-5 / x
x = 7.63 x 10^-5 / 0.00001
x = 7.63 x 10^-1 m
x = 0.763 m
**Answer:**
The uncertainty in the position of the electron is 0.763 m, which is approximately equal to 19.2 x 10^-2 m (option C).
- Mass of the electron (m) = 9.1 x 10^-31 kg
- Velocity of the electron (v) = 300 m/s
- Accuracy = 0.001% = 0.00001
**Uncertainty principle:**
The uncertainty principle, also known as Heisenberg's uncertainty principle, states that it is impossible to simultaneously determine the exact position and momentum of a particle with absolute certainty.
Mathematically, the uncertainty principle can be expressed as:
Δx * Δp ≥ h/4π
where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck's constant.
**Calculating the uncertainty in momentum:**
The momentum of an electron can be calculated using the formula:
p = m * v
where p is the momentum, m is the mass, and v is the velocity.
Substituting the given values, we get:
p = (9.1 x 10^-31 kg) * (300 m/s)
p = 2.73 x 10^-28 kg m/s
**Calculating the uncertainty in position:**
Using the uncertainty principle equation, we can rearrange it to solve for Δx:
Δx = (h/4π) / Δp
Substituting the values, we get:
Δx = (6.626 x 10^-34 J s / (4π)) / (2.73 x 10^-28 kg m/s)
Δx = 7.63 x 10^-7 m
**Converting the uncertainty to a percentage:**
To convert the uncertainty to a percentage, we can use the formula:
Uncertainty percentage = (Δx / x) * 100
where Δx is the uncertainty and x is the position.
Substituting the values, we get:
Uncertainty percentage = (7.63 x 10^-7 m / x) * 100
Given that the uncertainty percentage is 0.001%, we can write it as 0.00001.
0.00001 = (7.63 x 10^-7 m / x) * 100
0.00001 = 7.63 x 10^-5 / x
x = 7.63 x 10^-5 / 0.00001
x = 7.63 x 10^-1 m
x = 0.763 m
**Answer:**
The uncertainty in the position of the electron is 0.763 m, which is approximately equal to 19.2 x 10^-2 m (option C).
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Community Answer
Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving...
Δx∗mΔv=h/4π
Δv=300*0.001/100
= 3*10
-3
now put the values u'll get the ans
h=6.63*10
h=6.63*10
34
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Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving with a velocity of 300 ms-1, accurate upto 0.001% will be:a)1.92 x 10-2mb)3.84 x 10-2mc)19.2 x 10-2md)5.76 x 10-2mCorrect answer is option 'C'. Can you explain this answer?
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Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving with a velocity of 300 ms-1, accurate upto 0.001% will be:a)1.92 x 10-2mb)3.84 x 10-2mc)19.2 x 10-2md)5.76 x 10-2mCorrect answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving with a velocity of 300 ms-1, accurate upto 0.001% will be:a)1.92 x 10-2mb)3.84 x 10-2mc)19.2 x 10-2md)5.76 x 10-2mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Uncertainty in the position of an electron (mass 9.1 x 10-31kg) moving with a velocity of 300 ms-1, accurate upto 0.001% will be:a)1.92 x 10-2mb)3.84 x 10-2mc)19.2 x 10-2md)5.76 x 10-2mCorrect answer is option 'C'. Can you explain this answer?.
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