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(a) An electron in the ground state of the hydrogen atom moves at an average speed of $5 \times 10^{6} \mathrm{m} / \mathrm{s}$. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is $5.29 \times 10^{-11} \mathrm{m},$ comment on your result. The mass of an electron is $9.1094 \times 10^{-31} \mathrm{kg}$.(a) An electron in the ground state of the hydrogen atom moves at an average speed of $5 \times 10^{6} \mathrm{m} / \mathrm{s}$. If the speed is known to an uncertainty of 1 percent, what is the uncertainty in knowing its position? Given that the radius of the hydrogen atom in the ground state is $5.29 \times 10^{-11} \mathrm{m},$ comment on your result. The mass of an electron is $9.1094 \times 10^{-31} \mathrm{kg}$.

Uncertainity in the position $=1.16 \times 10^{-9} \mathrm{m}$a . Uncertainity in the position is almost 500 times larger than the radius of hydrogen atom. So it is very difficult to find the electron in the hydrogen atom.$\Delta x=7.23 \times 10^{-27} \mathrm{m}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton College

University of Central Florida

University of Maryland - University College

Lectures

04:49

In chemistry and physics, electronic structure is the way the electrons of an atom are arranged in relationship to the nucleus. It is determined by the subshells the electrons are bound to, which are in turn determined by the principal quantum number ("n") and azimuthal quantum number ("l"). The electrons within an atom are attracted to the protons in the nucleus of that atom. The number of electrons bound to the nucleus is equal to the number of protons in the nucleus, which is called the atomic number ("Z"). The electrons are attracted to the nucleus by this mutual attraction and are bound to the nucleus. The electrons within an atom are attracted to each other and this attraction determines the electron configuration. The electron configuration is described by the term symbol, which is the letter used to identify each subshell.

16:45

In physics, the wave–particle duality is the concept that every object or process, no matter how large or how small, behaves as both a wave and a particle. The wave–particle duality is one of the central concepts in quantum mechanics.

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(a) An electron in the gro…

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In the ground state of hyd…

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Calculate the uncertainty …

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Suppose that the uncertain…

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What is the uncertainty in…

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Suppose the velocity of an…

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for part A, whereas the calculate minimum uncertainty for an electron on the ground state of a hydrogen atom. If the speed is known to an uncertainty of 20% formula, will use Delta X mm Delta U must be greater than or equal to h over four pi. It's isolated for the uncertainty here felt the X greater than equal to each over for high I am Delta U. This would be substituting in Delta X greater than or equal to 6.63 times 10 to the negative 34 Jules per second for pie, the mass of an electron is nine point 109 times 10 to the negative 31 killer jewels and we're told that the uncertainty is 20% of its speed is known to uncertainty of 20%. So 0.20 times 5.0 times 10 to the six meters and solving for adults x. We find that it is equal to the minimum uncertainty. The position seven to times 10 to the negative 10 m. So that would be the minimum uncertainty in the position of the electron of a hydrogen atom. For part B, right? Where else to calculate the uncertainty in measuring the momentum or the uncertainty in the position of the baseball. They're poor formula here. It's going to be and were given momentum. Adult X. I'm still to peace. Momentum greater than or equal to each over four pi I am rearranging here Delta X greater than or equal to each over four pi times change in momentum. Delta X greater than equal to 663 times 10 to the negative 34 jewels per second for pie. And the momentum is, um, we have to calculate the momentum. The momentum we find is equal to 10 times 10 to the negative seven, which is the It has an uncertainty. Uncertainty 1.0 times, 10 to the negative, seven times the Mo mentum 67 kg meters per seconds and this would be equal to Delta X. The uncertainty in the baseball's position is 0.98 times 10 to the negative 27 m

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