TEST 3 Flashcards
What is a wave?
A wave is an oscillation or periodic movement that can transport energy from one point in space to another. (kinetic energy is transferred through matter (the rope, water, or air) while the matter remains essentially in place.)
electromagnetic waves consist of
an electric field oscillating in step with a perpendicular magnetic field, both of which are perpendicular to the direction of travel. These waves can travel through a vacuum at a constant speed of 2.998 × 10^8 m/s, the speed of light (denoted by c)
waves are characterized by
a wavelength, a frequency and an amplitude
wavelength
lamda; the distance between two consecutive peaks or troughs in a wave measured in meters
frequency
Hz, v or nu; the number of wave cycles that pass a specified point in space in a specified amount of time (seconds.) A cycle corresponds to one complete wavelength.
amplitude
corresponds to the magnitude of the wave’s displacement. The amplitude is related to the intensity of the wave, which for light is the brightness, and for sound is the loudness.
speed of a wave
The product of a wave’s wavelength (λ) and its frequency (ν
for electromagnetic radiation in a vacuum, speed is equal to
the fundamental constant, c
what is the relationship between wavelength and frequency
inversely proportional. As the wavelength increases, the frequency decreases.
what happens when two or more waves come into contact?
they interfere with one another
standing waves
remain constrained within some region of space. A system with fixed end points such as this restricts the number and type of the possible waveforms. This is an example of quantization, in which only discrete values from a more general set of continuous values of some property are observed.
nodes
waves displaying more than one-half wavelength) all have one or more points between the two end points that are not in motion called nodes. number of nodes= n-1
what is a blackbody?
A blackbody is a convenient, ideal emitter that approximates the behavior of many materials when heated. It is “ideal” in the same sense that an ideal gas is a convenient, simple representation of real gases that works well, provided that the pressure is not too high nor the temperature too low. BUT the theoretical curves did not show a peak, and absurdly showed the intensity becoming infinitely large as the wavelength became smaller, which would imply that everyday objects at room temperature should be emitting large amounts of UV light. This became known as the “ultraviolet catastrophe” Planck resolved this by restricting the vibrational energies to discrete values for each frequency, he could derive an expression for blackbody radiation that correctly had the intensity dropping rapidly for the short wavelengths in the UV region.
E=
hc/lamda
Planck’s constant (a.k.a. h)
h= 6.626 ×× 10−34 joule seconds (J s)
a wave’s energy depends on its
intensity (which depends on the number of photons striking the surface within a given time period.) bc the number of electrons ejected within in a given time period was seen to increase as the brightness increased. So, the greater the number of incoming photons, the greater the likelihood that they would collide with some of the electrons.
increasing the brightness of incoming light ____ the number of ejected electrons
increases
increasing the frequency of incoming light can ____ the number of ejected electrons
increase
does increasing the brightness of light have an effect on the KE of the ejected electrons?
Increasing the brightness of incoming light has no effect on the kinetic energy of the ejected electrons. Only energy, not the number or amplitude, of the photons influences the kinetic energy of the electrons.
increasing the frequency of incoming light ___ the KE of the ejected electrons
increases. Frequency is proportional to energy and inversely proportional to wavelength. Frequencies above the threshold value transfer the excess energy into the kinetic energy of the electrons.
energy of an electron
𝐸=−𝑘𝑍^2/𝑛2
when an electron increases distance from the nucleus, it’s energy ___
increases
The discrete energies (lines) in the spectra of the elements result from
quantized electronic energies.
The energies of electrons (energy levels) in an atom are described by
quantum numbers: integer numbers having only specific allowed value and used to characterize the arrangement of electrons in an atom.
the intensity of a wave is related to its ____
amplitude
speed of a wave can be calculated with
The product of a wave’s wavelength (λ) and its frequency (ν), λν, is the speed of the wave. Thus, for electromagnetic radiation in a vacuum, speed is equal to the fundamental constant, c.
c=λν
einstein on the photoelectric effect
Einstein argued that the quantized energies that Planck had postulated in his treatment of blackbody radiation could be applied to the light in the photoelectric effect so that the light striking the metal surface should not be viewed as a wave, but instead as a stream of particles (later called photons) whose energy depended on their frequency, according to Planck’s formula, E = hν (or, in terms of wavelength using c = νλ, 𝐸=ℎ𝑐𝜆E=hcλ ). Electrons were ejected when hit by photons having sufficient energy (a frequency greater than the threshold). The greater the frequency, the greater the kinetic energy imparted to the escaping electrons by the collisions. Einstein also argued that the light intensity did not depend on the amplitude of the incoming wave, but instead corresponded to the number of photons striking the surface within a given time period. This explains why the number of ejected electrons increased with increasing brightness, since the greater the number of incoming photons, the greater the likelihood that they would collide with some of the electrons.
photoelectric effect
electrons could be ejected from the clean surface of a metal when light having a frequency greater than some threshold frequency was shone on it. Surprisingly, the kinetic energy of the ejected electrons did not depend on the brightness of the light, but increased with increasing frequency of the light. Since the electrons in the metal had a certain amount of binding energy keeping them there, the incident light needed to have more energy to free the electrons. According to classical wave theory, a wave’s energy depends on its intensity (which depends on its amplitude), not its frequency.
Each emission line consists of
a single wavelength of light, which implies that the light emitted by a gas consists of a set of discrete energies
Johann Balmer was able to derive
an empirical equation that related the four visible wavelengths of light emitted by hydrogen atoms to whole integers.
1/λ=k(1/4 - 1/n^2)
Johannes Rydberg
generalized Balmer’s work and developed an empirical formula that predicted all of hydrogen’s emission lines, not just those restricted to the visible range, where, n1 and n2 are integers, n1 < n2, and 𝑅∞R∞ is the Rydberg constant (1.097 ×× 107 m−1).
bohr
as the electron’s energy increases (as n increases), the electron is found at greater distances from the nucleus.; derived a theoretical expression for the Rydberg constant,
de Broglie argued that
Bohr’s assumption of quantization can be explained if the electron is considered not as a particle, but rather as a circular standing wave such that only an integer number of wavelengths could fit exactly within the orbit
2𝜋𝑟=𝑛𝜆
Heisenberg uncertainty principle:
It is fundamentally impossible to determine simultaneously and exactly both the momentum and the position of a particle
