Discuss how the observation of blackbody radiation, the photoelectric effect, and atomic line spectrum contributed to the development of quantum theory.
The spectrum of the hydrogen atom has a limited number of wavelength components.
The development of quantum mechanics was the result of two revolutionary ideas.
Discuss the wave functions of a particle in a onedimensional box.
An electron microscope is used to produce an image of two neurons.
At the end of the 19th century, some observers of the scientific / within a principal shell believed that it was nearly time to close the books on the field energies.
The main work left to be done was to ground-state electron configurations of apply this body of physics to such fields as chemistry atoms.
An explanation of the periodic table to predict the ground of certain details of light emission and a phenomenon known as the photo state electron configuration of its atoms were only a few fundamental problems left.
The beginning of a new golden age of physics was spelled out by the solution to these problems, rather than marking an end to the study of physics.
Classical physics is not good enough to explain phenomena at the atomic and molecular level.
This chapter explains how electrons are described through features known as quantum numbers and electron orbitals.
The model of atomic structure developed here will explain many of the topics discussed in the next several chapters: periodic trends in the physical and chemical properties of the elements, chemical bonding, and intermolecular forces.
Understanding the electronic structures of atoms will be gained by studying the interactions of radiation and matter.
The chapter begins with background information about the effects of radiation on the body.
The best way to learn in this chapter is to focus on the basic ideas of atomic structure, which are illustrated in the in-text examples.
Some of the Are You Wondering features and portions of Sections 8-5, 8-7, and 8-9 are of interest to you.
There are two types of radiation, Electromagnetic Radiation and Electromagnetic Radiation.
Waves have been experienced in a small boat on a large body of water.
The wave moves across the water, and the disturbance lifts the boat and allows it to fall.
Let's use a simpler example to show some important ideas and terminology about waves--a traveling wave in a rope.
Imagine tying one end of a rope to a post and holding the other end in your hand.
You have marked a small part of the rope with red ink.
You set up a wave motion in the rope as you move your hand up and down.
The colored segment moves up and down as the wave travels along the rope.
A wave's length is an important characteristic.
The product of the length of a wave and the Frequency in a rope shows how far the wave front travels in a unit of time.
The figure is called a wave.
The magnetic field component lies in a plane with the wavelength of the wave.
The electric field is the distance between two charged particles.
The electric field can be detected by the crests.
Direction propagation of magnetic and electric fields.
The electric field component wavelength is shorter than the Magnetic field component wavelength.
There is a magnetic field in the area.
Radio waves are a form of motion.
Water waves are also waves that are caused by a first radiation.
The electrons are in atoms.
Smaller units, including those listed below, are also used.
The angstrom is not an SI unit.
The wavelength of the radiation is shorter for high frequencies and longer for low frequencies, as shown in Figure 8-3.
Only a small portion of the entire spectrum can be seen from violet at the shortest wavelength to red at the longest wavelength.
The frequencies and wavelength of some forms of radiation are also indicated.
The light from the lamp has a wavelength.
The wavelength of the light from nanometers to meters is converted to m s-1 in the equation.
We solve for n by rearranging it to the form c>l.
The units of l should be meters.
Rearrange equation to form n and solve for n.
The need to change the units of l is the most important element here.
Many electronic devices have the light from red LEDs.
A typical light source is a light emitting device.
amplitude, wavelength, frequency, and speed are just some of the properties that we will use the most.
Another characteristic of radiation is described next, which will be used to discuss atomic structure later in the chapter.
Waves emerge from the points of impact of the two stones if two pebbles are dropped close together into a pond.
The two sets of waves intersect and there are places where the waves disappear and places where the KEEP IN MIND waves persist.
When the waves are in that destructive interference step, their crests and troughs coincide.
The highest crests and deepest troughs in the water are produced by the waves.
When the waves meet in a way that the peak of one phase by more or less than wave occurs at the trough of another, the waves cancel and the water is not completely flat.
An everyday illustration of interference occurs.
Sunlight contains all the colors of the rainbow.
When the grooves of the CD reflect the different wavelength components of the colors, they travel slightly different distances.
Phase differences are created by the angle at which we hold the CD to the light source.
For a given angle between the incoming and reflected light, all colors cancel except one, because the light waves in the beam interfere with each other.
As we change the angle of the CD to the light source, we see different colors.
The physical picture and mathematics of interference and diffrac are the same for water waves and electromagnetic waves.
The speed of light in any medium is lower than in a vacuum.
The speed in different media is different.
Light is bent when it passes from one medium to another.
When a beam of white light is dispersed through a transparent medium, the wavelength and refraction are involved.
A device called a frequency doubler is used to pass red laser light through.
When "white" light is passed through a glass prism, the red light is the least controlled and gives us the most.
Between red and violet are the other colors of the visible spectrum.
The medium dispersion is water droplets.
Experiments involving the interaction of light and matter led to the development of quantum theory.
Scientists had to reformulate the physical laws that govern the behavior of particles at the atomic scale to explain the results of these experiments.
In this section, we look at a few of the experiments and discuss how they contributed to the development of important new ideas and the biggest scientific revolution of the past 100 years.
We know that hot objects emit light of different colors, from the dull red of an electric-stove heating element to the bright white of a light bulb.
A continuous color spectrum can be created by the dispersal of light from a hot object.
A complete explanation of iron was not provided by classical physics.
When the energy increases from one allowed value to another, it increases by a tiny jump.
A red-hot object has a group of atoms on the surface of the heated object that have the same frequencies.
He used his theory to show the distribution of frequencies with temperature and radiation at all temperatures.
The higher the frequencies of the radiation, the greater the energy.
This is summa, and it can be rized by what we now call Planck's equation.
Ludwig Boltzmann had created an equation to account for the distribution of speeds.
Boltzmann showed that the relative chance of finding a molecule with a particular speed was related to its energy.
The results of the analysis of blackbody radiation were assumed to have been based on the Boltzmann distribution law.
The relative chance of an energy nhn is proportional to radiation within eight weeks.
After a few weeks, the assumption that the energy of the oscillators in the light-emitting source cannot have the most strenuous work of my values leads to excellent agreement between theory and experiment.
The existence of separate energy levels and quanta in a physical system was a new experience for scientists when they made the quantum hypothesis.
The transfer of energy was continuous and there were no limits to the energy of the system.
It's not surprising that scientists were initially skeptical of the quantum hypothesis.
It couldn't be accepted as a general principle until it had been tested on other applications.
After the quantum hypothesis was applied, it became a great new scientific theory.
Albert Einstein's explanation of the photoelectric effect was the first of these successes.
The Photoelectric Effect was discovered in the 19th century.
The photoelectric effect only occurs when the incident light has a certain threshold value.
Classical wave theory could not explain these observations.
Albert Einstein showed that they are what would be expected with a particle interpretation of radiation.
The photon energy is absorbed by light-matter interactions.
The threshold frequency is the lowest that the light can escape from a photoelectric photoelectric effect, and any energy in excess of the surface is the work function of the emitted photoelectrons.
The mini cannot accumulate the energy mum energy needed to extract an electron from a metal's surface because the electron work function is represented by the symbol PS.
The discussion that follows is based on the experimental setup shown in Figure 9.
We have observed the travel to the upper plate and set up an electric circuit to measure the simultaneous absorption of photoelectric current through an ammeter.
No current flows if the frequencies are below the threshold, even if the molecule absorbs one photon.
No photoelectric current is produced.
There is a photoelectric current if the light is weak.
If the threshold value is greater than n, the photoelectric current appears.
Light intensity is related to the number of photons arriving at a point per unit time.
The photoelectrons have a second circuit set up to measure their speed.
There is a potential difference between the photoelectric metal and the open-grid electrode in this circuit.
electrons must pass through the openings in the grid and onto the upper plate The approaching electrons are slowed down by the negative potential on the grid.
When the potential difference between the grid and metal is increased, the photoelectrons are stopped at the grid and the current ceases to flow through the ammeter.
Experiments of the type just described show that Vs is pro portional to the light intensity but not the frequency.
He is better known as p. A photon is like a particle in that it is a carrier of both energy and momentum, but it has no mass.
Einstein's expression relates the energy and momentum of a particle.
m0 is the rest mass of the particle.
The mass of a particle is measured when it is at rest with respect to the person making the measurement.
The expression is reduced to E for a photon.
Section 8-4 shows that the expression p = h>l applies to all particles.
The equation h>l helps us understand the effect of a photon and an electron colliding.
The change in wavelength that occurs when light is scattered by electrons in atoms in a crystal was first observed in 1923.
The Compton effect provides more confirmation that light has particle-like entities that can transfer momentum to other particles.
The minimum quantity of work and energy needed to extract an electron from a metal's surface are represented by the work function, PS.
Einstein's model states that light of Frequency n0 consists of just enough energy to liberate electrons.
Since the work function is a characteristic of the metal used in the experiment, n0 is also a characteristic of the metal.
When a photon of energy hn strikes an electron in the metal's surface, some of the energy is used to free the electron, and the rest is used to impart energy to the liberated electron.
The number of photoelectrons increases with the intensity of light, which indicates that we should associate light intensity with the number of photons arriving at a point per unit time.
The wavelength of light needed to see hydrogen atoms is 91.2 nm.
When light is shone on a sample of hydrogen atoms, it emits electrons.
We need the frequencies of the radiation to use the equation.
After expressing the wavelength in meters, we can get this from equation 8.1.
The equation was written for one photon of light.
If we have the energy per photon, we can convert it to a per-mole basis.
The Frequency of the Radiation should be calculated first.
The energy of a single photon is calculated.
When the energy of a single photon is expressed in SI units, the energy is small and difficult to interpret.
The internal energy and enthalpy changes of chemical reactions are similar in magnitude to the light's 493.6 kJ/mol energy content.
The protective action of ozone in the atmosphere comes from ozone's absorption of UV radiation.
chlorophyll absorbs light at energies of 3.056 and 10-19 J> photon.
If the light source is an electric discharge passing through a gas, only certain colors are seen in the spectrum.
If the light source is a gas flame, the flame may have a distinctive color indicative of the metal ion present.
In each case, the emitted light produces a spectrum consisting of only a limited number of components, which are observed as colored lines with dark spaces between them.
The light source is a lamp.
When an electric discharge is passed through a lamp, helium atoms emit light.
The light is dispersed by a small slit.
There are two sources of light emission: hydrogen gas and neon gas.
The light is emitted when the compounds of the alkali metals are excited.
Tom was recorded on photographic film.
A thin line appears as an image of the wavelength component.
There are five lines in the spectrum of helium that can be seen by the eye.
A kind of atomic finger Bunsen designed a print for each element.
Robert Bunsen developed a special gas burner for his first spectroscope and used it to identify elements.
They discovered some studies in 1860.
During the solar eclipse of 1868, the spectrum was observed to interfere with the spectrum on Earth.
A spectrograph is a camera used to photograph photographic film.
The device is called a spectroscope.
The hydrogen spectrum has been studied extensively.
The light from the hydrogen lamp appears to be purple.
The red light is the main component of this light.
There are three other lines in the visible spectrum of atomic hydrogen, a violet line, and a greenish-blue line.
The wavelength of the greenishblue line is obtained.
Astronomers have seen the ultraviolet spectrum of white stars before.
The name of the series is the Balmer series.
We will see if this is the case.
Balmer's equation was found to be a special case of the Rydberg for mula.
106 m-1 is H.
It is believed that only a limited number of energy values are available to excited gaseous atoms.
The search for an answer to this question provided scientists with a great opportunity to learn about the structures of atoms but also led them to one of the greatest discoveries of modern science, quantum theory.
When comet Shoemaker-Levy 9 crashed into Jupiter, scientists looked at the event with telescopes.
The four lines are not visible to the untrained eye.
The electrons in an atom are arranged outside the nucleus of an atom according to the Rutherford model of the nuclear atom.
The negatively charged electrons would be pulled into the positively charged nucleus if they were stationary.
The electrons must be moving.
If it is assumed that electrons move around the nucleus like planets, there is a problem.
Classical physics says that electrons are constantly speeding up.
The electrons would be drawn closer to the nucleus by losing energy.
An atom emits energy as a photon when an electron falls from a larger than normal circle to a smaller than normal circle.
There was no physical justification for this quantization physics.
He deduced it from the equation.
By using classical theory and imposing a quantization condition, Bohr was able to derive equations for the energies and radii of the allowed orbits.
H En is the number 1, 2, and 3.
10-18 J. H RH is 2.17868.
The energy is restricted to specific values.
The situation in which the electron is free of the nucleus is called q.
The emission spectrum of the hydrogen atom is explained in the next section using an equation.
The Bohr model is very successful.
The model is problematic.
It can't be generalized to explain the emission spectrum of atoms with more than one electron.
The model is an uneasy mixture of classical physics and unjustifiable quantization conditions.
None of the experimental facts could be explained by using only classical physics.
Modern quantum theory replaced Bohr's theory in the late 19th century.
quantum mechanics can be used to generate quantization.
It isn't assumed or imposed as a condition, as was done by Bohr.
The model of the hydrogen atom based on quantum mechanics does not include the circular orbits that are so prominent in Bohr's model.
The quantum leap from classical physics to the new quantum physics was spurred by the fact that the hydrogen atom model is wrong.
The energies allowed for a hydrogen atom are severely restricted by the Assess Equation.
An electron in a hydrogen atom has an energy of -4.45
The diagram is called an energy-level diagram.
The order of the allowed energy levels is shown in a diagram.
The first three lines of the Balmer series are shown here.
The electrons in excited atoms fall from higher energy levels to the ground state.
These lines are exposed to the sun.
The hydrogen atom is ionized.
The difference in energy between the two levels is called a unique quantity of energy.
The wave length of a line in the emission spectrum of the hydrogen atom is calculated using equations.
The differences between energy levels are limited because of the number.
Only certain frequencies are observed for the lines.
The wavelength of the line is related to the transition from n to n.
The atom emits a photon when it transitions from a higher to a lower energy level.
The magnitude of the energy difference between the two levels is called Ephoton.
The data for the equation is ni and nf.
The color of the line is determined by the energy difference between C/E and the number of hydrogen atoms.
The greater the number of atoms, the greater the intensity of the transition.
The energy change for the atom is negative because of the transition that occurs.
Students forget to use the absolute value of C/E when calculating a negative frequency.
Negative values for n or l are not appropriate because frequencies and wavelength are positive quantities.
Determine the wavelength of light absorbed by an electron transition in a hydrogen atom.
Refer to Figure 8-13 to determine which transition produces the longest wavelength line in the hydrogen spectrum.
A spectrum of emission is obtained when individual atoms in a collection of atoms are excited to different states of the atom.
The atoms relax to states of lower energy by emitting light waves.
In Figure 8-14(b), we show an alternative method in which we pass white light through a sample of atoms in their ground states and then pass the emerging light through a prism.
Figure 8-14 can help us understand how the light is absorbed by the atom.
In the case of emission, we have the numbers Ei and hn.
We have the numbers Ei + hn and hn - Ei for the Absorp tion.
The same information about the quantized energy levels of a system can be obtained by either emission or absorption spectroscopy.
Other considerations influence the choice of which technique to use.
If the sample has a relatively small number of atoms, emission spectroscopy might be the best technique.
If sensitivity isn't an issue, absorption spectroscopy might be the best technique.
The absorption spectrum is less complicated than the emission spectrum.
An excited sample will contain atoms in a variety of states, each being able to drop down to any of several lower states.
An absorbing sample is cool and transitions can only be done from the ground state.
In absorption from cold hydrogen atoms, the Balmer series is not seen.
The energy of a photon absorbed by a hydrogen atom is just enough to remove the electron from the n level.
The energy of the free electron is zero and the atom is ionized.
The energy is dependent on the magnitude of the charges and the separation between them.
The energy of the electron ionized from a Li2+ ion in its ground state can be determined using a photon.
The electron has a different energy than the other one.
Determine the wavelength of light emitted in an electron transition from n to n.
The transition for an unknown hydrogen-like ion is 16 times more frequent than the hydrogen atom.
In the previous section, we pointed out that interpretation of atomic line spectrum was a difficult problem for classical physics and that Bohr had some success in explaining the emission spectrum for the hydrogen atom.
He was unable to explain the features of the hydrogen emission spectrum because his model was not correct.
A decade or so after Bohr's work on hydrogen, two landmark ideas stimulated a new approach to quantum mechanics.
The new quantum mechanics are considered in the next section.
Einstein suggested that light has particle-like properties, which are displayed through photons.
The wave theory of light is the best way to understand dispersion of light into a spectrum by a prism.
He was particles of matter.
He was reluctant to commit to a physical interpre velocity of meters per second, even though he had no doubt about the mass and reality of the phase wave.
He units of mass, length and length preferred to let his work stand as a formal scheme whose physical con time, which is why he left his definition of the phase wave vague in the concluding sentences of his thesis.
beams of particles, such as units kg m2 s-2 are possible if matter waves exist for small particles.
The interference pattern is observed if the distance between the objects that the waves scatter from is the same as the wavelength of the radiation.
X-rays have a wavelength of 1 A (100 pm) and are highly energetic.
The Diffraction of X-rays by metal foil demonstrated the wave properties of electrons.