Explanation Write the expression for Heisenberg uncertainty principle. Δ x Δ p x ≥ ℏ 2 Here, Δ x is the uncertainty in the position of the electron s position Δ p x is the uncertainty in the measurement of electrons momentum For n = 1 , The uncertainty in the position is the radius of the n = 1 Bohr orbit for hydrogen. Write the condition for the minimum uncertainty product. Δ x Δ p x = ℏ 2 (1) Substitute r 1 for Δ x in equation (1) to get Δ p x . Δ p x = h 2 × 2 π r 1 Substitute 6.626 × 10 − 34 J ⋅ s for h and 0.529 × 10 − 10 m for r 1 in above equation to get Δ p x . Δ p x = 6.626 × 10 − 34 J ⋅ s 4 × 3.14 ( 0.529 × 10 − 10 m ) = 1.0 × 10 − 24 kg ⋅ m / s Write the expression for the Bohr’s angular momentum condition for n = 1

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Chapter 39, Problem 39.70P

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The simultaneous minimum uncertainty of the corresponding momentum component of an electron in n=1 and compare this with the magnitude of the electron in the n=1 Bohr orbit.

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Chapter 39, Problem 39.69P

Chapter 39, Problem 39.71P

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Suppose that the uncertainty of position of an electron is equal to the radius of the n = 1 Bohr orbit for hydrogen. Calculate the simultaneous minimum uncertainty of the corresponding momentum component, and compare this with the magnitude of the momentum of the electron in the n = 1 Bohr orbit. Discuss your results.

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Find expectation value of position and for an electron in the ground state of hydrogen across the radial wave function. Express your answers in terms of the Bohr radius a.

Chapter 39 Solutions

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Ch. 39.2 - Prob. 39.2TYU Ch. 39.3 - Prob. 39.3TYU Ch. 39.4 - Prob. 39.4TYU Ch. 39.5 - Prob. 39.5TYU Ch. 39.6 - Prob. 39.6TYU Ch. 39 - Prob. 39.1DQ Ch. 39 - Prob. 39.2DQ Ch. 39 - Prob. 39.3DQ Ch. 39 - When an electron beam goes through a very small...Ch. 39 - Prob. 39.5DQ

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The simultaneous minimum uncertainty of the corresponding momentum component of an electron in n = 1 and compare this with the magnitude of the electron in the n = 1 Bohr orbit.

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The simultaneous minimum uncertainty of the corresponding momentum component of an electron in n=1 and compare this with the magnitude of the electron in the n=1 Bohr orbit.

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