The probability density of finding a particle somewhere along the the probability density is . For, the probability density decreases by a factor of each time the distance from the origin is doubled. What is the probability that the particle will be found in the interval
probability to finding a particle in
Calculate the value C by using normalization condition,
now, calculate probability of finding particle in interval 2mm as follows,
A particle is described by the wave function c1x2 = b cex/L x … 0 mm ce-x/L x Ú 0 mm where L = 2.0 mm.
a. Sketch graphs of both the wave function and the probability density as functions of x.
b. Determine the normalization constant c.
c. Calculate the probability of finding the particle within 1.0 mm of the origin. d. Interpret your answer to part b by shading the region representing this probability on the appropriate graph in part a
a. Starting with the expression for a wave packet, find an expression for the product
for a photon.
b. Interpret your expression. What does it tell you?
c. The Bohr model of atomic quantization says that an atom in an excited state can jump to a lower-energy state by emitting a photon. The Bohr model says nothing about how long this process takes. You'll learn in Chapter 41 that the time any particular atom spends in the excited state before emitting a photon is unpredictable, but the average lifetime of many atoms can be determined. You can think of as being the uncertainty in your knowledge of how long the atom spends in the excited state. A typical value is . Consider an atom that emits a photon with a wavelength as it jumps down from an excited state. What is the uncertainty in the energy of the photon? Give your answer in .
d. What is the fractional uncertainty in the photon's energy?
Heavy nuclei often undergo alpha decay in which they emit an alpha particle (i.e., a helium nucleus). Alpha particles are so tightly bound together that it's reasonable to think of an alpha particle as a single unit within the nucleus from which it is emitted.
a. nucleus, which decays by alpha emission, is in diameter. Model an alpha particle within nucleus as being in a onc-dimensional box. What is the maximum specd an alpha particle is likely to have?
b. The probability that a nucleus will undergo alpha decay is proportional to the frequency with which the alpha particle reflects from the walls of the nucleus. What is that frequency (reflections/s) for a maximum-speed alpha particle within a nucleus?
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