Quantum Mechanics & Spectroscopy

Answers

Unit 57: Particle Waves

Q57.1) 0.24 nm

Q57.2) 6.63 x 10⁻²⁵ kg m/s

Q57.3) 0.22 nm

Q57.4) 3300 m/s

Q57.5) From the Rayleigh criterion, resolution is limited by diffraction. Smaller wavelengths diffract less, so result in better resolution (finer details). Optical microscopes use visible light with wavelengths of 400nm to 700nm, whereas electrons accelerated in microscopes have de Broglie wavelengths on the order of 0.01nm to 1nm. Since electrons have smaller wavelengths than visible photons, they diffract less and therefore result in better resolution.

Unit 58: Wavefunctions & Probability Density

Q58.1)

a)

b)

c) x = L/6, L/2, 5L/6

d) x = 0, L/3, 2L/3, and L (ie near the 1st, 4th, 7th, and 10th carbons)

e) 0.9 nm

f) 1.48 nm⁻¹

g) 2.2%

h) 1/3 or 33.3%