Problem 9.24 If you take the model in Ex. 4.1 at face value, what natural frequency do you get? Put in the actual numbers. Where, in the electromagnetic spectrum, does this lie, assuming the radius of the atom is 0.5 Å? Find the coefficients of refraction and dispersion, and compare them with the measured values for hydrogen at 0°C and atmospheric pressure: A = 1.36 × 10-4, B = 7.7 x 10-15 m².

What is the minimum frequency of a photon required to ionize: (a) a He+ ion in its ground stare? (b) A Li2+ ion in its first excited state?

Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen atom) and its kinetic energy is equal to the ground state energy of the hydrogen atom in Bohr's model (13.6 eV). (a) What is the minimum uncertainty of its momentum? What fraction of its momentum is it? (b) What would the uncertainty in kinetic energy of this electron be if its momentum were equal to your answer in part (a)? What fraction of its kinetic energy is it?

A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation, hr the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming that this is part of the Balmer series, determine the principal quantum number of the initial state, (b) What is unreasonable about this result? (c) Which assumptions are unreasonable 01 inconsistent?

Show that (x,t)=Asin(kxt) and (x,t)=Acos(kxt) do not obey Schrödinger's time-dependent equation.

Check Your Understanding A particle With mass m is moving along the x-axis in a given by the potential energy function U(x)=0.5m2x2. Compute the (x,t)*U(x)(x,t). Express your answer in terrns of the time-independent wave function, (x).

Sketch the potential energy function of an electron in a hydrogen atom, (a) What is the value of this function at r=0 ? in the limit that r=? (b) What is unreasonable or inconsistent with the former result?

A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (C) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

Compute |(x,t)|2 for the function (x,t)=(x)sint, where is a real constant.

Check Your Understanding The vibrational frequency of the hydrogen iodide HI diatomic molecule is 6.691013Hz. (a) What is the force constant of the molecular bond between the hydrogen and the Iodine atoms? (b) What is the energy of the emitted photon when this molecule makes a transition between adjacent vibration energy levels?