**Problem Statement:**A proton is contained in an infinite one-dimensional box with a minimum kinetic energy of 7.9 MeV. The potential energy is zero inside the box. Show the steps needed to determine the width of the box.**Solution Steps:**1. **Understanding the Quantum System:** - The proton is confined in a one-dimensional infinite potential well. - The eigenvalues of energy for a particle in such a box are given by: \[ E_n = \frac{n^2 h^2}{8mL^2} \] Where: - \( n \) is the principal quantum number (n = 1, 2, 3, ...), - \( h \) is Planck’s constant, - \( m \) is the mass of the proton, - \( L \) is the width of the box.2. **Given Conditions:** - Minimum kinetic energy \( E_1 = 7.9 \text{ MeV} \).3. **Determine the Width of the Box:** - Using the expression for energy, substitute \( E_1 = 7.9 \text{ MeV} \) and \( n = 1 \): \[ 7.9 \times 10^6 \text{ eV} \times 1.6 \times 10^{-19} \text{ J/eV} = \frac{h^2}{8mL^2} \] - Solve for \( L \): \[ L = \sqrt{\frac{h^2}{8m \times 7.9 \times 1.6 \times 10^{-13}}} \] - Use constants: - \( h = 6.626 \times 10^{-34} \text{ J}\cdot\text{s} \), - \( m = 1.673 \times 10^{-27} \text{ kg} \).4. **Final Calculation:** - Substitute the values for \( h \), \( m \), and the kinetic energy to calculate \( L \).This calculation determines the width of the box necessary to achieve the given kinetic energy for the proton in an infinite potential well.

Solution:-Given thatminimum kinetic energy (KEmin)=7.9 MeV

Answered: A proton is contained in an infinite…

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A proton is contained in an infinite one-dimensional box with a minimum kinetic energy of 7.9 MeV. The potential energy is zero inside the box Show the steps needed to determine the width of the box