The acidic hydrogen in benzoic acid is IR active at 3573 cm 1. Assuming this hydrogen behaves as a quantum harmonic oscillator, calculate the following (your final answer must be a numerical value). Hints: use the mass of a single hydrogen atom in kilograms and use the frequency, v, in s. 1. ao 2. a 3. az 4. as 5. Normalization constant for wo(x). 6. Normalization constant for w₁(x). 7. Normalization constant for w₂(x). 8. Normalization constant for ws(x).

1.Calculate the kinetic energy of an electron ejected from the surface of a sample of Yttrium when the metal is subjected to photons having a wavelength of 375 nm.Show your answer in 3 sig figs.

19. List the quantum numbers of all states in the 4d subshell of hydrogen in the (n, l, me, ms) basis and in the (n, l, j, mj) basis.

a. Normalize the wavefunction Ψ(x) = 1 in a space of 0 ≤ x ≤ ℓ b. Find the probability of finding the particle in the subspace [0,ℓ/2 ] c. Find the most-likely position of the particle in entire space d. Find the most-likely position of the particle in the subspace [0,ℓ/3 ]

please answer #9

Show that at long wavelengths, Planck’s radiation law (as shown) reduces to the Rayleigh–Jeans law (as shown).

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…