Chapter 13 – Electrons in Atoms

CP Chemistry

The four models of the atom that you will be accountable for knowing and drawing, including the name of the scientist for each model.

13.1 Models of the AtomJohn Dalton (1766-1844) advanced atomic theory with the following four principles (p. 107)1. All elements are composed of tiny particles called

atoms.2. Atoms of the same element are identical. The atoms of any one

element are different from those of any other element.3. Atoms of different elements can physically mix together or can

chemically combine with one another in simple whole-number ratios to form compounds.

4. Chemical reactions occur when atoms are separated, joined or rearranged. Atoms of one element, however, are never changed into atoms of another element as a result of a chemical reaction.

NOTE: Dalton’s theory considers the atom to be a solid, indivisible mass. This theory continued for nearly 50 years after Dalton.

13.1 Atomic Models - Thompson• In 1897, Thompson was the first to suggest that the

electron was >1000 times smaller than the atom.• He claimed the chemical properties of atoms, ions

and molecules are related to the arrangement of electrons within them.

• J.J. Thompson (1856-1940) explained the electron position using the “plum pudding” model, which represented negatively charged electrons like plums in a lump of positively charged material, the pudding.

• His model didn’t say anything about the number of protons and electrons matching for a neutral atom. It also said nothing about the arrangement of electrons or why it is relatively easy to strip one electron out of the plumb pudding to make ions.

13.1 – Atomic Models - Rutherford• You already learned about Rutherford’s

experiment in Ch. 5, involving gold foil.• He showed in the early 1900s that most of an

atom’s mass was distributed at the center of the atom in the small, positively charged nucleus.

13.1 Bohr Model

• After Rutherford, in 1913, Niels Bohr (Danish) proposed the electrons travel in definite orbits around the nucleus.

• Question: What prevents electrons from falling into the nucleus?

• Bohr’s answer: Electrons in a particular path have a fixed energy, so electrons do not lose energy and fall into the nucleus. Let’s see what he means by that….

• The student can stop at any point on the ramp. Her distance from the ground changes continuously.

• The student can stop only at certain points on a flight of stairs. Her distance from the ground is quantized.

• Similarly, atomic energy levels are like steps…the energies available to an atom do not form a continuum, they are quantized

Bohr Model• Bohr was right in describing the

fixed energy levels of electrons like a set of stairs.The lowest stair is the lowest energy level.– An electron can climb up or down only by going on the

stairs at fixed, discrete energy levels, but note that the distance (the energy) between stairs isn’t equal!

– You can’t stand between stairs, just as electrons cannot possess just any energy, they only exist at specific energy levels.

– A quantum of energy is the energy required to move an electron up one energy level. It is not a fixed number, because as you see, the steps aren’t all the same distance apart.

A little Bohr history• Bohr focused describing the electron. • Prior to the Bohr Model, the accepted model was one

which depicted the electron as an orbiting planet. • The flaw with the planet-like model is that an electron

particle moving in a circular path would be accelerating (centripetal acceleration).

• An accelerating electron creates a changing magnetic field. This changing magnetic field would carry energy away from the electron, eventually slowing it down and allowing it to be "captured" by the nucleus, but we don’t see that happening.

Absorption spectrum>Emission spectrum >

• Bohr built upon spectroscopic observations of atoms. • Spectroscopists noticed that an atom can only absorb certain

energies (colors) of light (the absorption spectrum) and once excited can only release certain energies (the emission spectrum) and these energies happen to be the same.

• Bohr used these observations to argue that the energy of an electron is "quantized." Quantized is a fancy word meaning only certain quantities of energy are allowed. This explanation addresses the true origin of light. Since only certain energy levels are allowed it is actually possible to diagram the atom in terms of its energy levels. In the animation below you will see a model of a Hydrogen atom and to the right of it, a Bohr energy level diagram.

Bohr Model

In general, the higher the energy level, the further away the electron is from the nucleus (n=1 lowest level, n=∞ highest level)• You can picture it being analogous to gravity and potential energy.

The higher an object is from the ground (its ground state) the higher the potential energy is.

• Except this is different because at infinitely far away, there is zero potential energy because there is no electrostatic attraction between the positive nucleus and the negative electron.

• So the “ground” state has the most negative potential energy, and the highest (at ∞ state) has zero potential energy.

• The stair step changes between energy levels gets smaller as you go away from the nucleus.

Schroedinger • Austrian physicist Erwin Schrӧdinger (1887-

1961) took the atomic model one step further. – He used quantum theory to write a 3-D equation that

describes the location and energy of the electron in the hydrogen atom.

– The modern quantum mechanics model is derived from the Schrӧdinger equation.

– Like the Bohr model, this equation restricts the energies to certain levels.

– Unlike the Bohr model, the model doesn’t restrict the location of the electron to a certain orbital. Instead it gives the probability of finding an electron at a certain location.

Quantum Mechanics - Schroedinger

• Probability – – Imagine a dart board that’s been used a lot. You’ll

probably see more holes near the center of the target than you do near the edges.

– Similarly, the probability of an electron being close to the nucleus is higher than the probability it is farther away.

– Question: What would be the probabilities for two electrons that are equal distances from the nucleus?

Quantum Mechanics - Schroedinger

• Probability – – The probability of finding an electron within a

certain volume of space around the nucleus can be represented by a fuzzy cloud.

– The cloud is denser where the probability is higher and less dense where probability is lower.

– In drawings it is the convention to show a cloud where the electron could be 90% of the time. The last 10% probability’s location goes out to an infinite distance from the nucleus.

Atomic Orbitals• The quantum mechanical model designates major energy

levels by principal quantum numbers, n=1,2,3,4• The distance from the nucleus increases with increasing n• Within each principal energy level, the electrons occupy

sublevels. (Refer to Table 13.1 on page 364)• Note that the number of sublevels = principal energy level #

Principal energy level

Number of sublevels

Type of sublevel

n=1 1 1s (1 orbital)

n=2 2 2s (1 orbital), 2p (3 orbitals)

n=3 3 3s (1 orbital), 3p (3 orbitals), 3d (5 orbitals)

n=4 4 4s (1 orbital), 4p (3 orbitals), 4d (5 orbitals), 4f (7 orbitals)

The Shape of Atomic Orbitals• Recall that in this model the electron path is not

necessarily a circular path so they can’t really be called orbits (which in the case of the planets are elliptical anyway)!

• In the quantum mechanical model, they are called atomic orbitals, but don’t take that to mean that they are necessarily circular (or elliptical)!

• Recall that the quantum mechanical model limits the description of an electron’s position to an area within an electron probability cloud.

• What is the shape of those clouds? Spherical or something else?

Shapes of s and p atomic sublevel orbitals

Can you describe the shape and location of each s and p orbital?.

p orbitals shown as “clouds”

Shape of d orbitals – 5 of them

Can you describe the shape of each orbital and explain how dxy is different than d x

2-y

2

f orbitals – 7 of them

Don’t panic – I’m not going to ask you to describe or be tested on the shape of these orbitals. This is just so you have seen them.

Quiz: How many s,p,d,f orbitals??• How many s orbitals per level are there?• 1• How many p orbitals per level are there?• 3• How many d orbitals per level are there?• 5• How many f orbitals per level are there?• 7• What’s the pattern?• s,p,d,f• 1,3,5,7 You’ll need that later, don’t forget it!

n=1 principal energy level details

• Let’s take n=1– It has only one sublevel, called 1s– 1s is spherical, which means the

probability of finding an electron is the same if you go out from the origin in the x,y or z direction (but the probability does vary with distance out from the nucleus).

– This isn’t true for p,d, or f orbitals because their shape is not spherical.

n=2 principal energy level details• Now let’s take n=2. It has two

sublevels, 2s and 2p.– The 2s orbital is spherical like the 1s,

and the three 2 p orbitals are dumbbell shaped.

– The 2p sublevel is higher energy than the 2s orbital and the three 2p orbitals (2px, 2py and 2pz) are equal energy.

– So all together for n=2, you have 2s 2s, 2px, 2py and 2pz

a total of four

n=3 and 4 principal energy level details• The third level, n=3 has 3 sublevels,

called 3s, 3p and 3d. All together this level has:– 3s, 3px, 3py, 3pz, 3dxy, 3dxz, 3dyz,

3dx2-y2, 3dz2 , a total of 9.• The fourth level n=4 has 4 sublevels, – 4s (1) – 4p (3) – 4d (5)– 4f (7)– This is a total of 16

This is the order in which the energy levels are filled as you go down the periodic table.

Start at the bottom, and work your way towards the top.

First four rows done here as an example.

Ga, Ge, As, Se, Br, KrSc,Ti,V,Cr,Mn,Fe,Co,Ni,Cu,ZnK, Ca

Al, Si, P, S, Cl, ArNa, Mg

B,C,N,O,F, NeLi, Be

H, He

Principal Quantum Number Trends• What did you notice about the relationship

between the principal quantum number and the total number of levels? See table below.

• Each orbitals can hold two electrons.• PQN Orbitals Total # of electrons

n=1 1 2n=2 4 8n=3 9 18n=4 16 32

13.2 Electron Configurations• In most natural configurations, change proceeds towards the

lowest possible energy state. • Things that are at a higher energy tend to go to lower energy

by themselves (e.g. if you drop a pencil, it will fall down to a state of lower gravitational potential energy. Same idea with electrons, but instead of a gravitational field its an electrical field between electrons and the protons in the nucleus).

• It works the same with the electrons in an atom. They occupy the lowest possible energy states first.

• Electrons don’t skip up to a higher energy state, leaving lower energy states open (unless they are given some external energy).

• This leads to the Aufbau principle

Three principles you must know(refer to pages 367-368 in text)

1. Aufbau principle2. Pauli exclusion principle3. Hund’s rule

The Aufbau Principle

1. Electrons enter orbitals of the lowest energy first.

2. The various orbitals within a sublevel of a principal energy level are always of equal energy.– Look at 2p, see how those 3

boxes are all at the same energy: px = py = pz .

– Look at 4f, see how those 7 boxes are all at the same energy.

zAufbau Diagram

Aufbau principle (continued)3. Within a principal energy

level, the s level is always the lowest– See how 3s < 3p < 3d– Verify 4s < 4p < 4d < 4f

4. The range of energy levels within one principal energy level can overlap in the range of energies held by an adjacent principal energy level– See how 3d > 4s– See how 4f > 5p

• Electrons do enter the orbitals of lowest energy first, but they do not follow a simple pattern beyond the first two energy levels due to the overlap of energy levels.

• On the Aufbau diagram, each box represents 1 atomic orbital.

If you follow the red arrows from the bottom of the page upwards, that is how electrons will fill the energy levels as they become available. For example, if I had 20 electrons, which energy levels would they fill?1s, 2s, 2p, 3s, 3p, 4s2 +2 +6 +2 +6 +2 = 20

And they would fill the sublevels in that order, as shown.

Order of filling subshells in the building-up of atomic electron configurations. (a) Relative energies of subshells at the time they are being filled. (b) Aid to remembering the order of filling subshells. All possible shells having the same n value are written on horizontal lines. Diagonal arrows from lower right to upper left are then followed to obtain the order of filling. (The only subshells shown are those which are partially or completely occupied in atoms that have so far been discovered.)

Pauli Exclusion Principle - Background• The concept of electron spin was developed by Samuel

Goudsmit and George Uhlenbeck in 1925 when they were graduate students in the Netherlands.

• They found that another quantum number was necessary to account for the details of emission spectra of atoms.

• When scientists studied the line spectra of many-electron atoms in detail, they noticed that lines that were originally thought to be single were actually closely spaced pairs.

• Uhlenbeck and Goudsmit proposed that electrons have an intrinsic property, called electron spin, that causes each electron to behave as if it were a tiny sphere spinning on its own axis (picture the Earth spinning). A spinning charge produces a magnetic field. The two opposite directions of spin therefore produce oppositely charged magnetic fields which lead to the splitting of spectral lines into closely spaced pairs.

Pauli Exclusion Principle• An atomic orbital (one box on the Aufbau diagram) can hold up to 2

electrons, one with each type of spin.• If 2 electrons occupy the same orbital, they must have opposite

spins. Spin is a quantum mechanical property of electrons and your textbook, dated 2002, says spins may be clockwise or counterclockwise. That is an oversimplified statement that has been further developed by modern physics, and is useful only as an elementary pictorial representation.

• A detailed discussion of spin would be a post-calculus college level discussion. So what you need to know is:

• There are only two possible values for spin: sz = +1/2 and sz = −1/2. These correspond to quantum states in which the spin is pointing in the +z or −z directions respectively, and are often referred to as "spin up" and "spin down".

Pauli Exclusion Principle• A vertical arrow indicates an electron and its spin direction.

This is what an orbital filled with two electrons should look like.

• When an orbital gets its first electron, it is customary to make that a “spin up” electron like this. The 2nd electron will be “spin down”.

• You cannot fill an orbital with two electrons with the same spin.

CANNOT DO EITHER OF THESE >>>

Hund’s Rule

• Hund’s rule: when electrons occupy orbitals of equal energy (for example 2px, 2py, 2pz) one electron enters each orbital before any orbital receives a second electron.– Example 3 electrons (symbol e- )

filling 3 orbitals of equal energy– What if 5 electrons had to go in the same 3 energy

levels? – If I put the 6th electron in like this is that right?

• Electrons fill orbitals such that it fills one sublevel and then moves on to the next sublevel.

• Note how 2px, 2py and 2pz each get 1 electron before any orbital in that sublevel gets two.

• Table 13.2 starts with H (one electron) and proceeds down to Na (with 11 electrons)

• Energy 1s < 2s < 2px = 2py = 2pz < 3s

Electron Configuration

Example• Let’s see how to load oxygen with 8 electrons:

• This can be shown in shorthand as 1s22s22p4

• If you add up all the superscripts it should equal the number of electrons for that atom.

• Online periodic table with this feature (go to orbital tab!) USE THIS TABLE TO SELF-TUTOR !!!

• http://www.ptable.com

1s 2s 2px 2py 2pz 3s

1 2 3 4 5 8 6 7

How to read electron configurations right off the periodic table

The one with the arrow pointing to it is Phosphorus. You can write the electron configuration by “reading” across the periodic table just like you would read a book, until you get to that point.

Phosphorus 1s22s22p63s23p3

To summarize:Phosphorus1s22s22p63s23p3

Now, since the configuration for Ne is the first part of the whole configuration: 1s22s22p6

Phosphorus can also be written in noble gas form like this[Ne] 3s23p3

Nickel 1s22s22p63s23p64s23d8

Can also be written in noble gas form like this[Ar]4s23d8

Write the electron configuration for this one

Gallium: 1s2 2s22p63s23p64s23d104p1

Do you see how you read across the rows like a book?Just stop reading at the element you are interested in.

Exceptional Electron Configurations• You can obtain correct electron configurations for the

elements up to vanadium (atomic number 23) by using the Aufbau diagram. If you were to do that for Chromium and Copper, you would get:– Cr 1s22s22p63s23p6 4s23d4

– Cu 1s22s22p63s23p64s23d9

– But the correct configurations are:– Cr 1s22s22p63s23p6 4s13d5

– Cu 1s22s22p63s23p6 4s13d10

– Why do you think these “oddballs” would do that?

• These arrangements give Cr a half-filled d sublevel and Cu a filled sublevel. Filled and ½ filled energy sublevels are more stable than partially filled sublevels.

13.3 Physics and Quantum Mechanics• Let’s go back to our discussion of

Schrӧdinger’s work from section 13.1.• Originally, Isaac Newton ~1700, thought that

light was made up of particles (you can think of it as a packet of light called a photon).

• By 1900, most scientists had changed to thinking of light as a wave phenomenon.

Gack!

Wave-particle duality• In a debate that dates back to the 17th century, light was

thought either to consist of particles (Newton) or of waves (Huygens). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, James Maxwell and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).

• “All particles” includes massless photons of light and electrons that have mass.

• This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely small wavelengths, wave properties usually cannot be detected

The Electro-magnetic Spectrum

Electromagnetic radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet light, x-rays and gamma rays.

The wave equation• All waves (water waves, sound waves, light) have the

following relationship:• Speed = wavelength x frequency• For light, it looks like this: • Where c = the speed of light: 3x108 m/sec.• λ (lambda) = the wavelength in meters for one cycle.• (nu) = the frequency in Hertz or cycles/sec or 1/sec.

– Hertz is abbreviated as Hz. You can omit writing “cycles”, because it is assumed to be understood.

• You may see the same equation written as v = λf.• If so, then v = speed (velocity) in m/sec, λ

= wavelength in meters and f = frequency in Hertz.• It’s the same thing either way, just different letters.

Let’s try a calculation • This kind of calculation may be new for you (or

for your use of your calculator) so let’s try one.• c = λν• c = the speed of light = 3.00 x 1010 cm/sec. (or expressed in meters, 3.00 x 108 m/sec).• If you are given a wavelength of 4.0x10-5 cm,

what is the frequency?

How do you do that on the calculator?

• Use the 2nd/EE button instead of typing x1010 on the calculator.

• Use the (-) sign at the bottom right corner of the calculator instead of the minus sign - to create the negative exponent.

• By using the EE button you can save yourself a lot of calculator errors because the calculator knows that 3E10 is the same as 3.00x1010

• Now we’ll do a sample on the document camera.

Waves: vocabulary

“in phase” means two points on the wave that are one

complete cycle apart.

What’s different about these two waves?

If this time period represents 1 second, what are the frequencies for the red and green waves? (2.5 and 7.5 Hz)

Visible spectrum• The visible spectrum of light varies from about 700

nm (red) wavelength to about 380 nm (violet) light in a continuous spectrum.

• The shorter wavelength light is the higher frequency light. The shorter wavelength light is also the higher energy light, as you know because you get sunburned by ultraviolet rays, not the red end of the spectrum.

• Sunlight consists of light that is a combination of all these colors (ROYGBIV) in a continuous spectrum of wavelengths, which can be separated by a prism, because each wavelength of light bends differently when it hits the prism.

The visible spectrum

R O Y G B I V

Quick Quiz

• Which color has the longest wavelength?• Red• Which color has the shortest wavelength?• Violet• Which color has the highest frequency?• Violet• Which color has the lowest frequency?• Red

Elements and emission spectra• Every element emits light when its electrons are

excited (energy added) by the passage of an electric discharge (electric current) through its gas or vapor.

• The element first absorbs this energy and electrons move up to higher energy levels. Then after some time, they lose that energy and emit a photon of light with exactly the amount of energy they are losing.

• If they lose a lot of energy, the light is violet.• If they lose the least energy, the light is red.• Any other colors are mid-level energy lost.

When an element emits photons of light, instead of a continuous spectrum light sunlight has, you will only see certain narrow bands of color being emitted, because there are only certain energies that are characteristic for that element.

While white light gives a continuous spectrum, atomic emission spectra consist of relatively few colored lines and are called line spectra or discontinuous spectra. Each line corresponds to a specific amount of energy being emitted.

Not in this order – you figure it out during the Flame Test Lab

The Quantum Concept and the Photoelectric Effect• Classical physics state that there is no limit to how small the

energy that may be lost by an object can be. If that was the case, the spectra emitted by an atom should be continuous, but they are not.

• Max Planck, in 1900, hypothesized that energy losses could not take on any value, but only certain discrete values. He noticed this because when iron was heated up, it changed from black to red to yellow to white and then blue as it got hotter.

• One model to think of this is like bricks building a wall. You can’t build the wall to be just any height. The height of the wall has to be a multiple of the height of one brick because you are not using infinitely small slices of bricks to build it.

• Planck hypothesized: Energy = h x ν

Planck’s constant

• Planck’s equation E = hν (that’s a nu, not a “v” (vee)) says that energy is equal to the frequency ν times a constant h, which is called Planck’s constant.• h = 6.6262 x 10-34 Joules x second (or J-s)• Recall a Joule is a unit of energy.• Therefore a small energy change, E, involves the emission of

low frequency ( low ν) energy.• A large energy change, E, involves the emission of high

frequency energy.• So Planck advanced the idea that energy was quantized, and

he was quickly followed by Einstein.

The photoelectric effect• In 1905, Einstein also was looking at light as a particle. He

proposed that light could be described as a quanta of energy that behaves as if it was a particle: – Light quanta are called photons.

• The energy of photons is given according to E = hν• He considered the photoelectric effect, shown below:

The photoelectric effect

Classical physics couldn’t explain this because they expected that if you shine a weak light on the surface, you should eventually collect enough energy to emit electrons. But for potassium metal, no amount of red light (low energy light) will cause any electrons to be emitted. But even a little bit of yellow light (higher energy light) would cause electrons to be emitted. Classical physics couldn’t explain that using wave theory.

Photoelectric cells

Think about it – we are now using light to create electricity, using the photoelectric effect.

Sunlight

Hydrogen

Helium

Mercury

UraniumSee a trend here?

Atomic Emission Spectrum- Explanation• For a hydrogen atom, the lines observed in the spectrum are

consistent with the Bohr theory that electrons can only exist in certain orbitals which have certain energy levels n=1,2,3 and so forth.

• If an electron is in its lowest energy level, n=1, then it is considered to be in its ground state (can’t go any lower than that).

• If the electron gains energy through an external source (like an electric field) it can be “excited” to a higher energy level, such as n=2,3,4…. The amount of energy it takes is a quantum of energy, hν, to raise the electron to a higher energy level.

• Then when the electron loses energy and falls back down to the ground state, that exact same amount of energy, hν, is released as a photon of light with that same energy (color).

• ONLY electrons in transition from higher to lower energy levels lose energy and emit light.

Recall energy = hνso higher energy >> higher frequency light

What do you notice about the relationship between the amount of energy lost and the wavelength of the light emitted? The higher the energy lost, the shorter the wavelength

Bohr model

• The Bohr-type model on the previous charts was partially satisfactory. It did explain the emission spectra of atoms and ions containing one electron.

• Eventually it was displaced by the quantum mechanical model, which is based on the description of the motion of material objects as waves.

Quantum Mechanics• How do you put this all together?• Light is absorbed or emitted in discrete packages.• Light behaves as a wave and also as a particle.• In 1924, Louis de Broglie asked the question: If light waves can

behave as waves or particles, then can particles behave like waves? He derived this equation for the wavelength of a moving particle.

• where h=Planck’s constant, m=mass, v=velocity of particle

• Using this equation you can calculate the wavelength of a moving particle. (Is your mind exploding yet?)

• For an electron travelling at the speed of light, the wavelength is calculated to be 2x10-10 cm = 2x10-12 m (close to the size of an atom at 10-10 m or a nucleus at 10-14).

Wait, what about a baseball instead?

• Ok, let’s see what DeBroglie’s equation predicts about a “particle” like a baseball?

• 200 grams mass, moving at 30 m/sec. • Use • The baseball ends up with a calculated wavelength of 10-32 cm. (or

10-34 m)• Are you able to see motion of the size of 10-32 cm using any

equipment of any kind? (no)• So to us, something large like a baseball looks like a particle and not

a wave because there is no way we could ever see or detect its wave motion.

• Even an electron with a wavelength of 2 x 10-10 cm (or 2x10-12 m) is certainly nothing we can see visually. Visible light has a wavelength between 380 and 700 nm (or 3.8x10-5 cm to 7.0x10-5 cm).

What is that?(Isn’t he pretty?)

Both a wave and a moving particle possess energy, momentum and wavelength .The photograph shows a highly magnified Drosophila fly, made with a scanning electron microscope which uses electrons instead of light.The resolution is so good because the wavelength of an electron (2x10-10 m) is so much smaller than the wavelength of visible light (4x10-7 to 7x10-7 m)

To summarize…

• DeBroglie’s prediction that matter exhibits both wave and particle properties was a paradigm shift in the way we describe the motion of subatomic particles, atoms and molecules. This new method is called Quantum Mechanics.

1. Classical mechanics adequately describes the motions of bodies much larger than atoms. It appears that these large items gain or lose energy in any amount, but really the quanta are SO SMALL compared to the energy of the large object that it appears to be a continuum.

2. Quantum mechanics describes the motions of subatomic particles and atoms as waves. These particles can only gain or lose energy in packets called quanta.

Heisenberg uncertainty principle• Werner Heisenberg, 1927, is responsible for the Heisenberg

uncertainty principle, which states that it is impossible to know exactly both the velocity and the position of the particle at the same time. – The more precisely you try to measure the velocity, the less

precisely you will be able to measure the location. – Conversely, the more precisely you try to measure the location,

the less you know about the velocity.• The uncertainty in the location of a baseball traveling at 30 m/s is

only about 10-21 cm, which is not measureable. In other words, you know where the baseball is.

• But if you try to measure the location of an electron, with a mass of 9.1 x 10-28g, moving at the speed of light, then the uncertainty in position is about a billion centimeters, which means you have no idea exactly where it is.