Translational motion in ID 2. Calculate a) the average square of linear momentum, b) the average...
Problem 3. Calculate a) the average momentum and b) the average position of a particle, of mass m in a one-dimensional box of length L by evaluating specific integrals.
Question # 7: Determine the numerical value of the square of the momentum motion for the particle in 1D box. (Hint: suppose that the square of the momentum of motion is a sharp property (until the reverse is proved!) (Answer: P: P =+ Question # 8: Calculate the degree of uncertainty in the momentum of motion and in the speed of a. Electron moves in a box of length 18. b. A hydrogen atom moves in a box of length...
P7D.6 Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction y,. (a) Without evaluating any integrals, explain why(- L/2. (b) Without evaluating any integrals, explain why (p)-0. (c) Derive an expression for ) (the necessary integrals will be found in the Resource section). (d) For a particle in a box the energy is given by En =n2h2 /8rnf and, because the potential energy is zero, all of this...
Consider translational motion of single molecule (mass = 5.314 * 10-26 kg) trapped in one-dimensional box potential ("particle in a box), which has a width of 5 cm. A) What is the energy difference between the two lowest quantized energy levels? B) The amount of classical translational thermal energy for a molecule confined in one dimension is 1/2kT where T is the temperature and k is the Boltzmann constant (1.381 * 10-23 J/K). If the temperature is 300 K, at...
Question # 1: Find the unit of energy in the energy expression of a free particle in 1-D box: Question # 2: A proton in a box is in a state n = 5 falls to a state n = 4 and loose energy with a wavelength of 2000 nm, what is the length of the box? (answer: 4 x 10 m) Question # 3: a. Consider an electron confined to move in an atom in one dimension over a...
Tutorial: Angular Momentum and Torque III. Angular Momentum The angular momentum of a point particle is defined by: L = ixp. Here, is a vector that points from the point of rotation (or point around which the angular momentum is calculated) to the location of the particle and p = mb is the linear momentum of the particle. A Your little brother Joey is playing with his toy airplane. The airplane is tied to a string and its motor makes...
The average kinetic energy of translational motion of a molecule, in equilibrium, is (3/2)kBT. What is the average of the velocity squared in pure oxygen (O2) at standard pressure (1 bar) and concentration 0.001 mole/L? Give answer in (m/sec)2 . (To determine the temperature, please use the equation of state for the ideal gas.)
According to ChemActivity 1, HF at 25oC has the following average energies: Translational: 3.72 kJ/mol Rotational: 2.48 kJ/mol Vibrational: 23.7 kJ/mol The HF internuclear distance is 92 pm. Mass of 19F = 18.9984 amu, mass of 1H = 1.0078 amu. The force constant of the HF bond is 2448 N/m. 9. What is the average translational energy per molecule? How many modes of translational energy storage are there? What is the average energy per mode of translational motion? If the...
A particle of mass m is subject to a doubly infinite square well, with widths L, located at (a/2, a/2). The eigenstate wave functions for this are v(x, y) = L, = a and centre %3D %3D sin () sin ("). nyTy a) Find an expression for the position operator in bra-ket notation. b) Find an expression for the momentum operator in bra-ket notation. c) The particle is initially in the state |) : for position and momentum to find...