Particle-on-a-Ring Example #1: Calculate Electron Probability

Particle-on-a-Ring Example #1: Calculate Electron Probability

Assessment

Interactive Video

Science, Mathematics

University

Hard

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The video tutorial explains how to calculate the probability of finding an electron between two points on a ring using the particle on a ring wave function. It covers setting the limits of integration for benzene, calculating the probability using wave functions, and simplifying the integral. The tutorial emphasizes using logic to verify probability calculations and concludes with a preview of future topics, including energy and angular momentum calculations.

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7 questions

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1.

OPEN ENDED QUESTION

3 mins • 1 pt

What is the probability of finding a π electron between Carbons one and three of benzene?

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2.

OPEN ENDED QUESTION

3 mins • 1 pt

How do you determine the limits of integration when calculating the probability of finding an electron on a ring?

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3.

OPEN ENDED QUESTION

3 mins • 1 pt

Explain the significance of the normalized wave function for a particle on a ring.

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4.

OPEN ENDED QUESTION

3 mins • 1 pt

What is the integral used to calculate the probability of finding an electron between two points?

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5.

OPEN ENDED QUESTION

3 mins • 1 pt

How does the concept of complex conjugates apply when calculating probabilities in quantum mechanics?

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6.

OPEN ENDED QUESTION

3 mins • 1 pt

What is the probability of finding an electron between one and four on a benzene ring?

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7.

OPEN ENDED QUESTION

3 mins • 1 pt

Discuss how the energy level K affects the probability calculations in quantum mechanics.

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