lecture 8 starlight and atoms. announcements homework 5 – due monday, feb 26 unit 23: rq 1, p 2,...

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Lecture 8 Lecture 8 Starlight And Atoms Starlight And Atoms

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Page 1: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Lecture 8Lecture 8Starlight And AtomsStarlight And Atoms

Page 2: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

AnnouncementsAnnouncements

Homework 5 – Due Monday, Feb 26Homework 5 – Due Monday, Feb 26• Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3• Unit 24: RQ 1, 2, TY 2Unit 24: RQ 1, 2, TY 2• Unit 25: RQ 1, P 2Unit 25: RQ 1, P 2• Unit 55: RQ 3, P 4Unit 55: RQ 3, P 4

Page 3: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Basic IdeaThe Basic Idea

Stars produce light.Stars produce light. Star light tells us a lot Star light tells us a lot

about the star it about the star it comes from.comes from.

NEED to use star light NEED to use star light to study stars because to study stars because the material from a the material from a star has never been star has never been collected for study!collected for study!

Page 4: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Where Does Star Light Come Where Does Star Light Come From?From?

The light we detect The light we detect from a star comes from a star comes from the star’s from the star’s photospherephotosphere..

The The photospherephotosphere consists of the consists of the glowing gases in glowing gases in the outer “surface” the outer “surface” of a star.of a star.

Page 5: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

How Can A Cloud Have A Surface?How Can A Cloud Have A Surface?

A photosphere is A photosphere is made of a thin gas, so made of a thin gas, so how can it be a how can it be a surface?surface?• A photosphere isn’t a A photosphere isn’t a

solidsolid surface like the surface like the Earth’s surface, BUT…Earth’s surface, BUT…

• It glows so brightly you It glows so brightly you can’t see through it to can’t see through it to the gases below.the gases below.

• It’s a surface in the It’s a surface in the sense you can’t see sense you can’t see under it, just like the under it, just like the surface of the Earth.surface of the Earth.

Page 6: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Why Does A Photosphere Glow?Why Does A Photosphere Glow?

A photosphere glows because it is A photosphere glows because it is very hot!very hot!

The hotter something is, the more The hotter something is, the more light it produces AND the higher light it produces AND the higher energy (on average) that light energy (on average) that light becomes.becomes.

Makes hotter objects look BRIGHTER Makes hotter objects look BRIGHTER and BLUER than cooler ones.and BLUER than cooler ones.

Page 7: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

What is Heat?What is Heat? To understand why To understand why

hot things glow, we hot things glow, we need to understand need to understand what heat is.what heat is.

HeatHeat is a way to is a way to measure how quickly measure how quickly and violently the and violently the atoms or molecules in atoms or molecules in a substance are a substance are vibrating.vibrating.

These vibrations These vibrations cause the atoms and cause the atoms and molecules to collide.molecules to collide.

Page 8: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Heat Creates “Free Electrons”Heat Creates “Free Electrons” In any substance In any substance

some of the atoms some of the atoms and molecules vibrate and molecules vibrate faster than others.faster than others.

The hotter something The hotter something is, the more violently is, the more violently its atoms and its atoms and molecules vibrate molecules vibrate on on averageaverage..

Some collisions Some collisions between between atoms/molecules are atoms/molecules are violent enough to violent enough to “bump” electrons off “bump” electrons off of their atoms. These of their atoms. These are called are called free free electronselectrons..

Colliding atoms sometimes create…

…a free electron

Page 9: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

More Heat Means More Free More Heat Means More Free ElectronsElectrons

Since a hotter Since a hotter substance has faster substance has faster moving atoms on moving atoms on average:average:• Collisions are more Collisions are more

frequent.frequent.• Collision are, on Collision are, on

average, more violent.average, more violent.• More collisions are able More collisions are able

to create to create free free electronselectrons..

So the hotter So the hotter something gets, the something gets, the more free electrons it more free electrons it has.has.

Cool gas … not many free electrons.

Hot gas … lots more free electrons.

Page 10: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Free Electrons Also Collide With Free Electrons Also Collide With AtomsAtoms

In a hot gas, the In a hot gas, the free electrons also free electrons also collide with each collide with each other, and the other, and the other atoms in the other atoms in the gas…gas…

These collisions These collisions accelerateaccelerate the the electrons (change electrons (change their speed and their speed and direction).direction).

Page 11: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Light Comes From Accelerated The Light Comes From Accelerated Electrons!Electrons!

When an electron is When an electron is acceleratedaccelerated it gives off it gives off light.light.• The more the electron is accelerated the more energy The more the electron is accelerated the more energy

the emitted light has.the emitted light has.• For light, higher energy makes bluer light.For light, higher energy makes bluer light.

Very low energy light is invisible: infrared, microwaves, and Very low energy light is invisible: infrared, microwaves, and even radio waves.even radio waves.

Low energy light looks red to us.Low energy light looks red to us. Light with more energy than red light looks orange. Even Light with more energy than red light looks orange. Even

more energy makes it look yellow, then green, then blue, more energy makes it look yellow, then green, then blue, then violet.then violet.

Light with even more energy than violet is ultraviolet (and Light with even more energy than violet is ultraviolet (and is invisible to us).is invisible to us).

X-rays and gamma rays have even more energy than X-rays and gamma rays have even more energy than ultraviolet.ultraviolet.

Page 12: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

More Accelerated Electrons Means More Accelerated Electrons Means More Light!More Light!

REMEMBER: The hotter something is, REMEMBER: The hotter something is, the more free electrons it has.the more free electrons it has.

So there are MORE collisions, and we So there are MORE collisions, and we make MORE light.make MORE light.

CONCLUSION:CONCLUSION:• A hotter substance will produce (on A hotter substance will produce (on

average):average): BLUER light (higher energy light)BLUER light (higher energy light) MORE light (more photons because there are MORE light (more photons because there are

more free electrons to make light)more free electrons to make light)

Page 13: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Blackbody RadiationBlackbody Radiation

The light (EM The light (EM radiation) produced by radiation) produced by free electrons in a hot free electrons in a hot object is called object is called blackbody blackbody radiationradiation..

““Hot” is relative! Hot” is relative! AnythingAnything above above absolute zero absolute zero produces produces somesome blackbody radiation.blackbody radiation.

Page 14: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Radiation LawsThe Radiation Laws

There are two natural laws (equations) There are two natural laws (equations) that describe Blackbody Radiation.that describe Blackbody Radiation.

How Bright Is The Light?How Bright Is The Light?• Stefan-Boltzmann LawStefan-Boltzmann Law::

E = E = T T44

• E = amount of light energy produced E = amount of light energy produced per per square metersquare meter from the object’s surface each from the object’s surface each second (in Watts/msecond (in Watts/m22))

• T = temperature of the surface (in Kelvin)T = temperature of the surface (in Kelvin) = 5.67 × 10= 5.67 × 10-8-8

Page 15: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Radiation LawsThe Radiation Laws What Color Is The What Color Is The

Light?Light?• Actually, light of Actually, light of allall colors is colors is

produced, but the most produced, but the most commoncommon color of light is color of light is given by given by Wein’s Law:Wein’s Law:

maxmax = 3,000,000 / = 3,000,000 / TT

maxmax is the wavelength of the is the wavelength of the most common color of light most common color of light (more photons are this (more photons are this wavelength than any other). wavelength than any other). The units are The units are nanometersnanometers!!

• T is the temperature (again, T is the temperature (again, in Kelvin)in Kelvin)

Page 16: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit
Page 17: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

What is this “Kelvin”?What is this “Kelvin”? There is a There is a

temperature that is so temperature that is so cold that atoms and cold that atoms and molecules stop molecules stop moving completely: moving completely: absolute zeroabsolute zero..• At -273ºC (or -459ºF)At -273ºC (or -459ºF)

Lord Kelvin invented a Lord Kelvin invented a new temperature new temperature scale, based on the scale, based on the Celsius scale, where Celsius scale, where the zero point is the zero point is absolute zero.absolute zero.

Page 18: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Kelvin ScaleThe Kelvin Scale

On the Kelvin scale, there are no On the Kelvin scale, there are no negative temperatures (no such thing as negative temperatures (no such thing as a temperature below absolute zero).a temperature below absolute zero).

Subtract 273 from the Kelvin Subtract 273 from the Kelvin temperature to get the Celsius temperature to get the Celsius temperature.temperature.

Unlike common temperature scales, Unlike common temperature scales, which are ratios based on two fixed which are ratios based on two fixed points, the Kelvin is an absolute unit of points, the Kelvin is an absolute unit of measure and so is not expressed in measure and so is not expressed in “degrees”.“degrees”.

Page 19: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Using The Radiation LawsUsing The Radiation Laws

The sun’s surface temperature is The sun’s surface temperature is 5,800 K. How much light energy 5,800 K. How much light energy comes from each square meter of comes from each square meter of the sun’s surface each second?the sun’s surface each second?

Solution:Solution:

E = (E = ( = 5.67 × 10 = 5.67 × 10-8-8)(5,800 K))(5,800 K)44

E = 64,164,532 W/mE = 64,164,532 W/m22

(The W stands for “Watts”)(The W stands for “Watts”)

Page 20: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Using The Radiation LawsUsing The Radiation Laws

What is the most common color of light What is the most common color of light the sun produces?the sun produces?

Solution:Solution:

maxmax = 3,000,000 / (5,800 K) = 3,000,000 / (5,800 K)

maxmax = 517 nm = 517 nm

(This is actually green light, but it is (This is actually green light, but it is mixed in with enough yellow that our mixed in with enough yellow that our eyes see this color as yellowish)eyes see this color as yellowish)

Page 21: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Daily Grade 8 – Question 1Daily Grade 8 – Question 1

The wavelength of maximum intensity The wavelength of maximum intensity that is emitted by a black body isthat is emitted by a black body is

A.A. proportional to temperature.proportional to temperature.

B.B. inversely proportional to temperature.inversely proportional to temperature.

C.C. proportional to temperature to the fourth proportional to temperature to the fourth power.power.

D.D. inversely proportional to temperature to the inversely proportional to temperature to the fourth power.fourth power.

Page 22: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

What color are the stars?What color are the stars? We can use Wein’s We can use Wein’s

Law to figure this one Law to figure this one out…out…

First, all stars produce First, all stars produce light at all colors! And light at all colors! And we see all colors we see all colors together as together as whitewhite!!

But, the fact that But, the fact that moremore photons of one color photons of one color are produced than any are produced than any other gives the white other gives the white light from the star a light from the star a tinge of colortinge of color..

Page 23: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

What color are the stars?What color are the stars? The coolest stars are The coolest stars are

around 3,000 Karound 3,000 K maxmax = 1,000 nm = 1,000 nm• That’s infrared light, That’s infrared light,

which means that in which means that in visible light the star visible light the star will produce more will produce more red photons than red photons than any other color.any other color.

• The star will look The star will look reddish-white.reddish-white.

Page 24: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

What color are the stars?What color are the stars?

The sun has a The sun has a temperature of temperature of about 5,800 K.about 5,800 K.maxmax = 517 nm = 517 nm

• Tinges the sun’s Tinges the sun’s white light white light yellow.yellow.

• The star will look The star will look yellow-white.yellow-white.

Page 25: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

What color are the stars?What color are the stars?

The hottest stars The hottest stars have temperatures have temperatures over 40,000 K.over 40,000 K. maxmax = 75 nm = 75 nm• This is ultraviolet This is ultraviolet

light.light.• In visible light the In visible light the

star produces more star produces more blue light than any blue light than any other color.other color.

• Makes the star look Makes the star look blue-white.blue-white.

Page 26: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Color IndexThe Color Index

So very hot stars So very hot stars are bluish, and are bluish, and very cool stars are very cool stars are reddish.reddish.

But how do we But how do we quantitatively quantitatively measure a star’s measure a star’s color.color.

In astronomy, use In astronomy, use the the color indexcolor index..

Page 27: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Color IndexThe Color Index ProcedureProcedure::

• Take a picture of a star Take a picture of a star through two different through two different color filters.color filters.

Two common ones to use Two common ones to use in astronomy is a blue (B) in astronomy is a blue (B) filter and a green “visual” filter and a green “visual” (V) filter.(V) filter.

• Measure the Measure the magnitudemagnitude of the star in each filter of the star in each filter (i.e. how bright it looks in (i.e. how bright it looks in each filter).each filter).

• Take the two magnitudes Take the two magnitudes and subtract them:and subtract them:

B – VB – VThis number is called the This number is called the “B-V Color Index”“B-V Color Index”

B band V band

Page 28: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Color IndexThe Color Index

Remember, the Remember, the brighterbrighter a star is the a star is the smallersmaller its magnitude! its magnitude!

A blue star:A blue star:• Looks brighter through the B filter than the V Looks brighter through the B filter than the V

one.one.• B-magnitude is B-magnitude is smallersmaller than V-magnitude. than V-magnitude.• B – V = small number – large numberB – V = small number – large number

= negative number= negative number• Blue stars have a Blue stars have a negative negative color indexcolor index

Page 29: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

The Color IndexThe Color Index

Remember, the Remember, the brighterbrighter a star is the a star is the smallersmaller its magnitude! its magnitude!

A red star:A red star:• Looks brighter through the V filter than the B Looks brighter through the V filter than the B

one.one.• V-magnitude is V-magnitude is smallersmaller than B-magnitude. than B-magnitude.• B – V = large number – small numberB – V = large number – small number

= positive number= positive number• Red stars have a Red stars have a positive positive color index.color index.

Page 30: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Daily Grade 8 – Question 2Daily Grade 8 – Question 2

The B - V color index of a star indicates The B - V color index of a star indicates itsits

A.A. total mass.total mass.

B.B. radius.radius.

C.C. chemical composition.chemical composition.

D.D. surface temperature.surface temperature.

Page 31: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

A Primer on AtomsA Primer on Atoms An atom contains:An atom contains:

• A A positive positive nucleus nucleus composed of two types composed of two types of particles:of particles:

ProtonsProtons – actually – actually have the positive have the positive charge.charge.

NeutronsNeutrons – no charge, – no charge, but same mass as but same mass as protons.protons.

Contains most of the Contains most of the atom’s mass.atom’s mass.

• ElectronsElectrons ( (negativenegative charge) that orbit the charge) that orbit the nucleus.nucleus.

Electrons have very Electrons have very little mass compared to little mass compared to protons and neutrons.protons and neutrons.

Page 32: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Daily Grade 8 – Question 3Daily Grade 8 – Question 3

Which subatomic particle has a negative Which subatomic particle has a negative charge?charge?

A.A. The electron.The electron.

B.B. The proton.The proton.

C.C. The neutron.The neutron.

D.D. Both the neutron and the proton.Both the neutron and the proton.

Page 33: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Atomic DensityAtomic Density

If you could fill a teaspoon just with material as dense as the matter in an atomic nucleus, it would weigh ~ 2 billion tons!!

Page 34: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Different Kinds of AtomsDifferent Kinds of Atoms• The kind of atom

depends on the number of protons in the nucleus.

Different numbers of neutrons ↔ different isotopes Most abundant: Most abundant:

Hydrogen (H), with Hydrogen (H), with one proton (+ 1 one proton (+ 1 electron).electron).

Next: Helium (He), Next: Helium (He), with 2 protons (and with 2 protons (and 2 neutrons + 2 el.).2 neutrons + 2 el.).

Page 35: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Daily Grade 8 – Question 4Daily Grade 8 – Question 4

Which of the following is true of an Which of the following is true of an atomic nucleus?atomic nucleus?

A.A. It contains more than 99.9% of an It contains more than 99.9% of an atom's mass.atom's mass.

B.B. It contains all of an atom's positive It contains all of an atom's positive charge.charge.

C.C. It contains no electrons.It contains no electrons.

D.D. All of the above.All of the above.

Page 36: Lecture 8 Starlight And Atoms. Announcements  Homework 5 – Due Monday, Feb 26 Unit 23: RQ 1, P 2, TY 3Unit 23: RQ 1, P 2, TY 3 Unit 24: RQ 1, 2, TY 2Unit

Next TimeNext Time

Read Units 25 and 55 (yes, I mean 55, Read Units 25 and 55 (yes, I mean 55, way towards the back. I did say we’d way towards the back. I did say we’d be jumping around in this book).be jumping around in this book).