Six Electrons Are in a Two-Dimensional Square Potential Energy Well

question 19

Multiple Choice

Six electrons are in a two-dimensional square potential energy well with sides of length L.The potential energy is infinite at the sides and zero inside.The single-particle energies are given by where n_x and n_y are integers.If a seventh electron is added to the system when it is in its ground state the least energy the additional electron can have is:

• A)2 (h²/8mL²)
• B)5 (h²/8mL²)
• C)8 (h²/8mL²)
• D)10 (h²/8mL²)
• E)13 (h²/8mL²)

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Definitions:

Fast Food

A type of food service that emphasizes minimal preparation time and quick service, often associated with preheated or precooked ingredients served in a packaged form for take-away.

Probability Mass Function

An operation that calculates the chance that a given discrete random variable precisely equals a certain value.

Probability Density Function

A mathematical function that describes the likelihood of a continuous random variable taking on a specific value.

Normal Distribution

A bell-shaped frequency distribution that is symmetrical about the mean, describing how many data points, given continuous variables, distribute in nature.