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Answer: (a) An electron in the ground state of the
Chapter 7, Problem 139P(choose chapter or problem)
(a) An electron in the ground state of the hydrogen atom moves at an average speed of \(5 \times 10^6~\mathrm{m/s}\). 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 \(9.1094 \times 10^{-31}~\mathrm {kg}\).
(b) A 3.2-g Ping-Pong ball moving at 50 mph has a momentum of \(\mathrm {0.073~ kg \cdot ~ m/s}\). If the uncertainty in measuring the momentum is \(1.0 \times 10^{−7}\) of the momentum, calculate the uncertainty in the Ping-Pong ball's position.
Questions & Answers
QUESTION:
(a) An electron in the ground state of the hydrogen atom moves at an average speed of \(5 \times 10^6~\mathrm{m/s}\). 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 \(9.1094 \times 10^{-31}~\mathrm {kg}\).
(b) A 3.2-g Ping-Pong ball moving at 50 mph has a momentum of \(\mathrm {0.073~ kg \cdot ~ m/s}\). If the uncertainty in measuring the momentum is \(1.0 \times 10^{−7}\) of the momentum, calculate the uncertainty in the Ping-Pong ball's position.
ANSWER:Step 1 of 3
(a)
From the given,
