Question

an electorn is confined to move between two rigid walls seperated by 20°A.the energy associated with the electron in first excited state will be

Answer 1

Answer:

MARK BRAINLIEST

Explanation:

Answer 2

The energy associated with an electron confined between two rigid walls separated by a distance of 20 Å can be determined by solving the Schrödinger equation for a one-dimensional particle in a box potential. The first excited state energy (En) for such a system can be expressed as:

En = h^2 * (π^2) / (2 * m * L^2) * (n^2),

where h is Planck's constant, m is the mass of the electron, L is the distance between the walls (20 Å), and n is the quantum number of the state, with n = 2 for the first excited state.

Substituting the given values, the energy associated with the electron in the first excited state can be calculated.

• The confinement of an electron between two rigid walls separated by a distance of 20 Å can be described by the quantum mechanics concept of a particle in a box. The particle in a box model provides a simple yet effective way to understand the behavior of a quantum particle in a confined region.
• In this model, an electron is assumed to be confined to a region between two rigid walls, represented by a box potential. The motion of the electron is restricted to the interior of the box, and the potential energy of the electron is constant everywhere inside the box, except at the walls where it is infinite. The Schrödinger equation is used to describe the wave function of the electron in the box, which represents the probability density of the electron's position.
• The energy levels of an electron in a box potential can be found by solving the Schrödinger equation for a one-dimensional particle in a box. The first excited state energy (En) for such a system can be expressed as:
• En = h^2 * (π^2) / (2 * m * L^2) * (n^2),
• where h is Planck's constant, m is the mass of the electron, L is the distance between the walls (20 Å), and n is the quantum number of the state, with n = 2 for the first excited state.
• The particle in a box model has important implications for the study of quantum mechanics and solid-state physics. It provides a simple way to understand the quantization of energy levels in a confined system and the concept of wave-particle duality. It also has applications in the design of quantum devices, such as quantum dots and quantum wells, which are used in the field of nanotechnology.
• In conclusion, the energy associated with an electron confined between two rigid walls separated by a distance of 20 Å can be determined using the particle in a box model. The first excited state energy can be calculated by solving the Schrödinger equation for a one-dimensional particle in a box and using the expression for En. This model provides a simple yet effective way to understand the behavior of a quantum particle in a confined region and has important implications for the study of quantum mechanics and solid-state physics.

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