1. Which of the following statements concerning particle in a box are true? You must justify each of your answers for full credit.

I) The energy of the particle can be equal to zero.

II) The wavelength (λ) is proportional to the length of the box (L).

III) As the length of the box (L) increases, the energy levels become closer together.

2. For the n=(last digit of your student ID+2) case for particle in a box and assuming the box is L long. Sketch a diagram representing your wavefunction.

a) The position(s) of least probability is/are_________ (in terms of L)

b) The positions(s) of maximum probability is/are _____________

c) The probability of finding the particle at the position L/2 is ______________

3. If you have an electron and a proton both in a box of same length L (justify your answer in each case)

a. The electron will have greater/smaller/the same energy

b. The wavefunction for the electron will have greater/smaller/the same amplitude

c. The spacing between energy levels for the electron will be greater/smaller/the same

4. Another acceptable wavefunction for the particle in a box is A(kx/L)²[1-mx/L]

What values do k and m have to be to make the wavefunction behave correctly at the corners of the box?

5. What would the normalization constant (A) be for the wavefunction above?

**Subject Chemistry Physical Chemistry**