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Chapter 4: Q48E (page 137)
The p0 is a subatomic particle of fleeting existence. Data tables don't usually quote its lifetime. Rather, they quote a "width," meaning energy uncertainty, of about 150MeV. Roughly what is its lifetime?
The lifetime is .
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(a) What is the range of possible wavelengths for a neutron corresponding to a range of speeds from 鈥渢hermal鈥� at(see Exercise) to.(b) Repeat part (a), but with reference to an electron.(c) For this range of speeds, what range of dimensions D would reveal the wave nature of a neutron? Of an electron?
Determine Fourier transform function A(k) of the oscillatory function.
A particle is 鈥渢hermal鈥� if it is in equilibrium with its surroundings 鈥� its average kinetic energy would be. Show that the wavelength of a thermal particle is given by
A crack between two walls is wide. What is the angular width of the central diffraction maximum when
(a) an electron moving at passes through?
(b) A baseball of mass and speed passes through?
(c) In each case, an uncertainty in momentum is introduced by the 鈥渆xperiment鈥� (i.e., passing through the slit). Specifically, what aspect of the momentum becomes uncertain, and how does this uncertainty compare with the initial momentum of each?
The energy of a particle of massbound by an unusual spring is.
(a) Classically. it can have zero energy. Quantum mechanically, however, though both andare "on average" zero, its energy cannot be zero. Why?
(b) Roughly speaking.is a typical value of the particle's position. Making a reasonable assumption about a typical value of its momentum, find the particle's minimum possible energy.
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