The wave function for the ground state of the harmonic oscillator is %0 (2) = Ce-mw/(2A)|z² where C is an arbitrary constant, ħ is Planck's constant divided by 27, m is the mass of the particle, w = √k/m, and k is the "spring constant" for the harmonic oscillator. Normalize this wave function. What is the (positive) value of C once this wave function is normalized? You will need the formula -az² Express your answer in terms of w, m, h, and T. ► View Available Hint(s) C= IT ΑΣΦ Xh √x √x x IXI X.10n

Calculate the wavelength of the photon needed to excite a transition between adjacent energy levels of a harmonic oscillator of effective mass equal to that of a proton(1.0078 me) and a force constant of 544 N/m.

5. Determine yy for each of the following wavefunctions: (i =V-1) a) y (x) = e b) y(0) = sin 0 +i cose c) w(x) = A · e*.

Consider a single particle with rest mass m residing in a one-dimensional space, x. This particle experiences a potential energy V(x) = ∞ for x a, and a potential energy V(x) = 0 for 0 < x < a. The solutions to the Schrödinger Equation for this system are 12. 2 Vn(x) : sin a where n is the state's quantum number. Show that the ground state wave function is normalized.

What is the lowest possible value of the angular momentum quantum number (l) when the magnetic quantum number (ml) is −1?

A particle rotating on the surface of a sphere with fixed r has the quantum numbers I = 3 and mj = 1. What is the magnitude of the angular momentum? V12 h O 12n? O 12h

Assume that for ¹H35 Cl molecule the rotational quantum number J is 11 and vibrational quantum number n = 0. The isotopic mass of ¹H atom is 1.0078 amu and the isotopic mass of 35 C1 atom is 34.9688 amu, k = 516 N · m¯¹, and x = 127.5 pm. Part E Calculate the period for vibration. Express your answer in seconds to three significant figures. Tvibrational = Part F Submit Previous Answers 1.12x10-14 s Correct Correct answer is shown. Your answer 1.1181.10-¹4 = 1.1181x10-14s was either rounded differently or used a different number of significant figures than required for this part. Calculate the period for rotation. Express your answer in seconds to four significant figures. Trotational = ΑΣΦ W ? S

Consider a particle trapped in a iD box with zero potential energy with walls at x = 0 and x = L. The general wavefunction solutions for this problem with quantum number, n, are: yn(x) = The corresponding energy (level) for each wavefunction solution is: n?h? En 8ml? a) Is the particle always uniformly distributed throughout the box? Explain your answer. b) Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. Follow from Ex 4.7 in the textbook, let's assume that the 1o electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this "molecular box", 2 electrons can occupy an energy level. What are quantum states that the electrons from this molecule can occupy in the ground state? What's the smallest frequency of light that can excite the electron? Briefly explain why. Note that the…