2. Using the back of the envelope estimate that o,op position and momentum of the electron along the radial direction with respect to the proton in a hydrogen atom, where the proton is considered to be infinitely massive and stationary at the origin: Estimate the ground state energy of the hydrogen atom. Remember that in the ground state, there is no contribution to kinetic energy due to the angular momentum of the electron. = ħ for minimal simultaneous uncertainties in the

The nucleus of a typical atom is 5.0 fm (1 fm = 10-15 m) in diameter. A very simple model of the nucleus is a onedimensional box in which protons are confined. Estimate the energy of a proton in the nucleus by finding the first three allowed energies of a proton in a 5.0-fm-long box.

4 Figure 39-25 shows three infinite potential wells, each on an x axis. Without written calculation, determine the wave function for a ground-state electron trapped in each well. U. 2L O L/2 -L/2 +L/2 (a) (b) (c) Figure 39-25 Question 4.

The energy level diagram for an electron in an infinite potential well. The diagram shows five possible transitions from an excited state to a lower state. Arrange the transitions in ascending order of the wavelength of the emitted photon.

Please Solve the problem question quantum physics.... With the step, thank u

4. Normalize the following wavefunctions 4 55 (a) v(x) = sin (#2); =sin(); for a particle in a 1D box of length L. (b) (2) = xe-z|2 (c) (x) = e(x²/a²)+(ikz) 5. In a region of space, a particle with mass m and with zero energy has a time- independent wave-function (x) = Ae-2/12, where A and L are constants. Use your knowledge of the Schrödinger equation to determine the potential energy V(x) of the particle. Plot the potential function? What is the minimum potential energy for the particle, if it is an electron and L = 1 fm? Is this potential repulsive or attractive?