Quantum Mechanical Model Of Atom

Step 1: Understanding the problem. In the case of a particle confined in a one-dimensional infinite potential well (also known as a particle in a box), the probability of finding the particle at any point within the box is proportional to the square of the wave function . For the ground state, the wave function is given by: where: - is the length of the box, - is the position within the box (ranging from 0 to ). Step 2: Calculating the probability. The probability of finding the particle in a specific region is given by the square of the wave function integrated over that region. The probability of finding the particle in the first half of the box is: Substitute the expression for : This integral can be solved, and the result is: Step 3: Conclusion. Thus, the probability of finding the particle in the first half of the box for the ground state is . Answer: Therefore, the probability of finding the particle in the first half of the box is .