15 May CALCULATE THE ENERGIES OF ITS FIRST THREE ENERGY LEVELS.
Heisenberg uncertainty principle
i)The electron of the hydrogen atom may be thought to be localized within about 0.10 nm around the nucleus. Treating this as the position uncertainty, determine the limit of uncertainty of velocity measurement of this electron.
ii) For a helium atom moving with thermal velocity at 298 K, the velocity was measured with an 10% precision. What is the limit on the precision of a simultaneous position measurement in this situation?
iii) A sophisticated electronic system determined the velocity of a billiard ball as 5.0000 ±0.0001m/s. The mass of the ball is 200 g. Estimate the uncertainty of position measurement.
b) An electron is confined to a one-dimensional region of 10nm length.
i) Calculate the energies of its first three energy levels.
ii) Calculate the wavelength of light that will be absorbed when electron is excited from first to second energy level.
c) The vibrations of the HCl molecule may be modeled by assuming the H atom is moving in a harmonic potential with a force constant of 514 N/m, while the Cl atom remains stationary. Calculate the absorption frequency and wavelength of the first absorption transition. Repeat calculations for DCl.
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