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Chapter 7: Q44E (page 281)
How many different 3d states are there? What physical property (as opposed to quantum number) distinguishes them, and what different values may this property assume?
There are five states in the case of 3d states.
The angular momentum could be 0 or or .
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A particular vibrating diatomic molecule may be treated as a simple harmonic oscillator. Show that a transition from that n=2state directly to n=0ground state cannot occur by electric dipole radiation.
Explicitly verify that the simple function can be made to satisfy radial equation (7-31), and in so doing, demonstrate what its angular momentum and energy must be.
An electron in a hydrogen atom is in the (n,l,ml) = (2,1,0) state.
(a) Calculate the probability that it would be found within 60 degrees of z-axis, irrespective of radius.
(b) Calculate the probability that it would be found between r = 2a0 and r = 6a0, irrespective of angle.
(c) What is the probability that it would be found within 60 degrees of the z-axis and between r = 2a0 and r = 6a0?
Classically, it was expected that an orbiting electron would emit radiation of the same frequency as its orbit frequency. We have often noted that classical behaviour is observed in the limit of large quantum numbers. Does it work in this case? (a) Show that the photon energy for the smallest possible energy jump at the “low-n-end” of the hydrogen energies is , while that for the smallest jump at the “high-n-end” is , where is hydrogen’s ground-state energy. (b) Use F=ma to show that the angular velocity of a classical point charge held in orbit about a fixed-point charge by the coulomb force is given by . (c) Given that , is this angular frequency equal to the minimum jump photon frequency at either end of hydrogen’s allowed energies?
The space between two parallel metal plates is filled with an element in a gaseous stale. Electrons leave one plate at negligible speed and are accelerated toward the other by a potential differenceapplied between the plates. As is increased from 0, the electron current increases more or less linearly, but when reaches 4.9 V , the current drops precipitously. From nearly 0 , it builds again roughly linearly as is increased beyond 4.9 V .
(a) How can the presence of the gas explain these observations?
(b) The Gas emits pure “light” when exceeds 4.9 V . What is its wavelength?
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