Which is the acceptable normalized wave function of particle in 1D box ans. Ψ = √(2/a).Cos(nπx/a) Ψ = -√(2/a).Sin(nπx/a) Ψ = - A.Sin(nπx/a) Ψ = √(2/a).Sin(nπx/a)

The acceptable normalized wave function of a particle in a 1D box is:

Ψ = √(2/a).Sin(nπx/a)

Here's why:

1. The wave function must be normalized. This means that the integral of the absolute square of the wave function over all space must be equal to 1. Both the sine and cosine functions can be normalized with the factor √(2/a), so this doesn't help us choose between the options.

2. The wave function must be zero at the boundaries of the box. This is because the particle cannot exist outside the box, so the probability of finding the particle at the boundaries must be zero. For a 1D box extending from x=0 to x=a, this means that the wave function must be zero at x=0 and x=a.

3. The cosine function is not zero at x=0 and x=a for all values of n. Therefore, the cosine options can be eliminated.

4. The sine function is zero at x=0 for all values of n, and it is zero at x=a for integer values of n. Therefore, the sine options are possible.

5. The sign of the wave function does not affect the physical interpretation, because the absolute square of the wave function is used to find the probability density. Therefore, both the positive and negative sine options are acceptable.

6. However, the option Ψ = - A.Sin(nπx/a) is not normalized, because it does not have the normalization factor √(2/a). Therefore, this option can be eliminated.

So, the only acceptable normalized wave function of a particle in a 1D box is Ψ = √(2/a).Sin(nπx/a).