An electron is in a 3p state in the hydrogen atom, given that the expectation value is 12.5a_0 What is the probability of finding the electron within +/- a_0 of your expectation value. (That is, in the range (r − a_0) < r < (r+a_0) where r is the expectation value from above. The answer should be 0.1991.

An electron in a hydrogen atom is approximated by a one-dimensional infinite square well potential. The normalised wavefunction of an electron in a stationary state is defined as *(x) = √√ sin (""). L where n is the principal quantum number and L is the width of the potential. The width of the potential is L = 1 x 10-¹0 m. (a) Explain the meaning of the term normalised wavefunction and why normalisation is important. (b) Use the wavefunction defined above with n = 2 to determine the probability that an electron in the first excited state will be found in the range between x = 0 and x = 1 × 10-¹¹ m. Use an appropriate trigonometric identity to simplify your calculation. (c) Use the time-independent Schrödinger Equation and the wavefunction defined above to find the energies of the first two stationary states. You may assume that the electron is trapped in a potential defined as V(x) = 0 for 0≤x≤L ∞ for elsewhere.

Explain each step

An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?