PHLA10H3 : Glossary of Terms

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mauvedonkey369

18 Apr 2011

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Abduction - a form of nondeductive inference, also known as inference to the best explanation. Principle and the only game in town fallacy are relevant to deciding how strong an abductive inference is. The strength of analogy arguments is an issue relevant to the argument of design and to the problem of other minds. Analytic an analytic sentence is one whose truth or falsehood is deductively entailed by definitions. Many philosophers have held that mathematical statements are analytic. If a sentence isn"t analytic it is synthetic. A posteriori a proposition that can be known or justified only be sense experience. An a posteriori argument is an argument in which at least one premises is an a posteriori proposition. A priori a proposition that can be known or justified independent of sense experience. An a priori proposition can be known or justified by reason alone (once you grasp the constituent concepts).

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Consider a traveling wave described by the formula

$y_1(x,t) = A \sin(k x - \omega t)$ .

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

Part A

Which one of the following statements about the wave described in the problem introduction is correct?

ANSWER:

The wave is traveling in the

direction.
The wave is traveling in the

direction.
The wave is oscillating but not traveling.
The wave is traveling but not oscillating.

Part B

Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0

this new wave should have the same displacement as y_1(x,t)

, the wave described in the problem introduction.

ANSWER:

$A \cos (k x - \omega t)$
$A \cos (k x + \omega t)$
$A \sin (k x - \omega t)$
$A \sin (k x + \omega t)$

The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation is linear in the amplitude of the wave.

Consider the sum of two waves , where is the wave described in Part A and is the wave described in Part B. These waves have been chosen so that their sum can be written as follows:

$y_{\rm s}(x,t) = y_{\rm e}(x) y_{\rm t}(t)$ .

This form is significant because , called the envelope, depends only on position, and depends only on time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall amplitude of the wave is written as part of .

Part C
Find and . Keep in mind that should be a trigonometric function of unit amplitude.

erinhyena808

The emergence of line spectra from a gas when a current passesthrough it was an observed phenomenon waiting for an explanation inthe early 20th century. The atomic line spectra coming fromelements such as hydrogen had been analyzed since the late 19thcentury. By studying the wavelength of the emerging radiation ofhydrogen, experimenters found (often by trial and error) that thewavelengths in those spectra were described by the formula

\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2}\right),
where R is known as the Rydberg constant. It has a value of R =1.097 \times 10^{7}\; \rm m^{-1}. The variables n_1 and n_2 areinteger numbers (n_1 = 1,2,3,4,\dots). As experiments continued,scientists began to see more and more characteristic lines emergingfrom the hydrogen spectrum. Each of them corresponded to awavelength predicted by this formula with some integer values forn_1 and n_2.

In 1913, Niels Bohr provided an explanation for the observationsmade in experiments by proposing that each electron in an atom hadonly certain allowable energy levels. Furthermore, he postulatedthat when an electron changed its energy level, it must emit orabsorb a single photon with the energy equal to the energydifference between the two levels.

With this interpretation, the variables n_1 and n_2 acquired newsignificance. Bohr's model predicted that n_2 was the initialenergy state of the atom (n_initial) and that n_1 was the finalstate of the atom (n_final). A photon with the predicted wavelengthwas created when an atom made a transition from its initial energystate to a lower final energy state. The equation now read

\frac{1}{\lambda} = R \left( \frac{1}{n_{\rm final}^2} -\frac{1}{n_{\rm initial}^2} \right).
Bohr's model also predicted that a photon of the appropriatewavelength (given by the same formula) could promote an atom from alower energy level to a higher one.

In this problem, we explore the photon characteristics necessaryfor transitions between energy levels in hydrogen and singlyionized {\rm He}^+, whose energy levels are accurately predicted bythe Bohr model.
What is the change in energy DeltaE of the hydrogen atom as theelectron makes the transition from the n=3 energy level to the n=1energy level?
Express your answer numerically in electron volts.

b. When an atom makes a transition from a higher energy level to alower one, a photon is released. What is the wavelength of thephoton that is emitted from the atom during the transition from n=3to n=1?
Express your answer numerically in angstroms.

c.

When the hydrogen atom makes the transition from the n=2 to the n=1energy level, it emits a photon. This photon can be absorbed by toa singly ionized helium atom ({\rm He}^+) in its second energylevel (n_{\rm initial} = 2), causing it to move to a higher energylevel. To what final energy level number n_final can the photonpromote the helium ion?

Note that {\rm He}^+ has two protons in its nucleus and a singleelectron.
Express your answer as an integer.

Please answer fully, Thank you
a.

PHLA10H3 : Glossary of Terms

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