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The momentum of the fastest electrons is measured as 6.63 10-25 kg X ms. If there is a 15 percent uncertainty in knowing the momentum what is the minimum error in knowing the position of the electrons?
Wiki User
∙ 13y ago
Just use the uncertainty principle: Δp*Δx=h/2π =>Δx=h/(Δp*2π)=1.06*10^(-9)m
Wiki User
∙ 13y ago
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What are the two parts of the Heisenberg uncertainty principle?
Heisenberg uncertainty principle states that , the momentum and the position of a particle cannot be measured accurately and simultaneously. If you get the position absolutely correct then the momentum can not be exact and vice versa.
Do electrons travel so fast that it is impossible to know their exact location?
No, that's not how it works. The Heisenberg Uncertainty Principle states that there is a limit to how precisely you can measure position and momentum simultaneously. Actually, it's not just about measuring, position and momentum are not DEFINED at the same time, with arbitrary precision.An electron can very well move slowly, but the Uncertainty Principle still applies.
What does the Heisenberg Uncertainty principle mean?
In any measurement, the product of the uncertainty in position of an object and the uncertainty in its momentum, can never be less than Planck's Constant (actually h divided by 4 pi, but this gives an order of magnitude of this law). It is important to note that this uncertainty is NOT because we lack good enough instrumentation or we are not clever enough to reduce the uncertainty, it is an inherent uncertainty in the ACTUAL position and momentum of the object.
What is important about the uncertainty principle?
Heisenberg's Uncertainty Principle is the principle that states that the momentum and the position of a quantum particle can not be simultaneously accurately known. This means that the more precisely you know the momentum, the less you know about the position and vice-versa.
When uncertainty in position of an electron is zero what will be uncertainty in momentum?
Werner Heisenberg's (1901-1976) uncertainty principle: ∆x∙ ∆(mv) ≥ h / 4π x = uncertainty; m = mass; v = velocity To solve for ∆x... ∆x = h / 4πm∆v
What are the two parts of the Heisenberg uncertainty principle?
Heisenberg uncertainty principle states that , the momentum and the position of a particle cannot be measured accurately and simultaneously. If you get the position absolutely correct then the momentum can not be exact and vice versa.
What momentum and position can't be measured at the same time?
The position and momentum of any sub-atomic particle cannot be measured at the same time due to the Heisenberg uncertainty principle. Simply put, it states that the more we know about one of the two properties, the less we know about the other.
Do electrons travel so fast that it is impossible to know their exact location?
No, that's not how it works. The Heisenberg Uncertainty Principle states that there is a limit to how precisely you can measure position and momentum simultaneously. Actually, it's not just about measuring, position and momentum are not DEFINED at the same time, with arbitrary precision.An electron can very well move slowly, but the Uncertainty Principle still applies.
According to the heisenberg uncertainty principle if the position of a moving particle is known what other cannot be known?
According to the Heisenberg uncertainty principle if the position of a moving particle is known velocity is the other quantity that cannot be known. Heisenberg uncertainty principle states that the impossibility of knowing both velocity and position of a moving particle at the same time.
What does the Heisenberg Uncertainty principle mean?
In any measurement, the product of the uncertainty in position of an object and the uncertainty in its momentum, can never be less than Planck's Constant (actually h divided by 4 pi, but this gives an order of magnitude of this law). It is important to note that this uncertainty is NOT because we lack good enough instrumentation or we are not clever enough to reduce the uncertainty, it is an inherent uncertainty in the ACTUAL position and momentum of the object.
Why is it that an electron cannot stay in the nucleus according to quantum mechanics?
The Heisenberg uncertainty principle shows that one cannot say precisely where an electron is located and precisely what its momentum (mass times velocity) is. More correctly, the uncertainty principle says that the uncertainty in the location of a particle times the uncertainty in its position is always greater than a certain constant number called Planck's constant. If an electron were inside the nucleus, which is a VERY small area, then we would know its position with great certainty. This means that the uncertainty in its momentum (and thus speed) must be tremendous. You can say that if an electron is confined to a small area, it speeds away from the area due to its large momentum. For this reason, electrons are distributed outside of the nucleus of an atom. To be more precise, they are almost entirely outside of the nucleus. There is still a VERY small probability to find electrons inside the nucleus. This probability can be both evaluated theoretically and measured (by indirect methods) experimentally.
Using De Broglie's wave-particle duality and Heisenberg's uncertainty principle Why is the location of an electron in an atom uncertain?
The position and momentum of electrons are correlated; if the accuracy of measurements increases one inevitably decreases to the other.
The Heisenberg Uncertainty Principle states that it is impossible to know?
For every quantum state, the standard deviation of it's position multiplied by the standard deviation of it's momentum has to be larger than or equal to the reduced Planck constant divided by two. σxσp ≥ hbar/2 This doesn't mean that you can't measure position and momentum at the same time. What it means is that the products of their deviations from their expectation values can't go lower than hbar/2, ie. there is a limit to the combined precision of the two measurements. It can also be shown that the combined precision of several other quantities have a lower limit, such as energy and time.
What is the position of the electrons in Bohr'smodel?
Defined orbits around nucleus, no uncertainty principle
What is important about the uncertainty principle?
Heisenberg's Uncertainty Principle is the principle that states that the momentum and the position of a quantum particle can not be simultaneously accurately known. This means that the more precisely you know the momentum, the less you know about the position and vice-versa.
When uncertainty in position of an electron is zero what will be uncertainty in momentum?
Werner Heisenberg's (1901-1976) uncertainty principle: ∆x∙ ∆(mv) ≥ h / 4π x = uncertainty; m = mass; v = velocity To solve for ∆x... ∆x = h / 4πm∆v
Using heisenberg's uncertainity principle prove the non existence of the electron inside the nucleus?
The Heseinberg's Uncertainty Principle states that you cannot know the position and momentum of a particle simultaneously. More rigorously stated, the product of the uncertainty of the position of a particle (Δx) and the uncertainty of its momentum (Δp) must be greater than a specified value: ∆x∆p ≥ (h/4π) Now, as the electron approaches the nucleus, it's uncertainty in position decreases (if the electron is 10nm away from the nucleus, it could be anywhere within a spherical shell of radius 10nm, but if the electron is only 0.1nm away from the nucleus, that area is greatly reduced). According to the Heisenberg uncertainty principle, if you decrease the uncertainty of the electrons position, the uncertainty in its momentum must increase. This increased momentum uncertainty means that the electron will be moving away from the nucleus faster, on average. Put another way, if we do know that at one instant, that the electron is right on top of the nucleus, we lose all information about where the electron will be at the next instant. It could stay at the nucleus, it could be slightly to the left or to the right, or it could very likely be very far away from the nucleus. Therefore, because of the uncertainty principle it is impossible for the electron to fall into the nucleus and stay in the nucleus. In essence, the uncertainty principle causes a sort of quantum repulsion that keeps electrons from being too tightly localized near the nucleus.
