# 16.2 Mass, energy, and the theory of relativity

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## Learning objectives

By the end of this section, you will be able to:

• Explain how matter can be converted into energy
• Describe the particles that make up atoms
• Describe the nucleus of an atom
• Understand the nuclear forces that hold atoms together
• Trace the nuclear reactions in the solar interior

As we have seen, energy cannot be created or destroyed, but only converted from one form to another. One of the remarkable conclusions derived by Albert Einstein (see Albert Einstein ) when he developed his theory of relativity is that matter can be considered a form of energy too and can be converted into energy. Furthermore, energy can also be converted into matter. This seemed to contradict what humans had learned over thousands of years by studying nature. Matter is something we can see and touch, whereas energy is something objects have when they do things like move or heat up. The idea that matter or energy can be converted into each other seemed as outrageous as saying you could accelerate a car by turning the bumper into more speed, or that you could create a bigger front seat by slowing down your car. That would be pretty difficult to believe; yet, the universe actually works somewhat like that.

## Converting matter into energy

The remarkable equivalence between matter and energy is given in one of the most famous equations:

$E=m{c}^{2}$

In this equation, E stands for energy, m stands for mass, and c , the constant that relates the two, is the speed of light (3 × 10 8 meters per second). Note that mass is a measure of the quantity of matter, so the significance of this equation is that matter can be converted into energy and energy can be converted into matter. Let’s compare this equation of converting matter and energy to some common conversion equations that have the same form:

$\text{inches}=\text{feet}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}12,\text{or cents}=\text{dollars}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100$

Just as each conversion formula allows you to calculate the conversion of one thing into another, when we convert matter into energy, we consider how much mass the matter has. The conversion factor in this case turns out not to be either 12 or 100, as in our examples, but another constant quantity: the speed of light squared. Note that matter does not have to travel at the speed of light (or the speed of light squared) for this conversion to occur. The factor of c 2 is just the number that Einstein showed must be used to relate mass and energy.

Notice that this formula does not tell us how to convert mass into energy, just as the formula for cents does not tell us where to exchange coins for a dollar bill. The formulas merely tell us what the equivalent values are if we succeed in making the conversion. When Einstein first derived his formula in 1905, no one had the faintest idea how to convert mass into energy in any practical way. Einstein himself tried to discourage speculation that the large-scale conversion of atomic mass into energy would be feasible in the near future. Today, as a result of developments in nuclear physics, we regularly convert mass into energy in power plants, nuclear weapons, and high-energy physics experiments in particle accelerators.

I l don't understand questions
which quesrions?
Ankit
How to make a telescope
Steve
***wikihow.com/Make-a-Telescope
Jennifer
optical mechanics
Astro
aptical
Nkateko
Which one has the ring
Saturn venue and even Jupiter all have rings the rings on Jupiter, however, aren't so easily noticed due to them only being viable through infrared
Hunter
visible *
Hunter
they each have three rings but not as you might think just think of them all as one big ring because that's basically what they are but they are desperate individual rings
Hunter
separate*
Hunter
can you tell me what is a quantam elighment? Lets see how many people give write answers
can you tell me what is a fomalhaut?
gdjm
Fomalhaut Is The Brightest Star In The Constalellation Of Piscis Austrinus.....
joe.
Tracy
Do You Mean Quantum Entanglement?
yes
gdjm
No Adam fomalhaut mean eye of universe
gdjm
quantum entanglement is when a husband has been married so long to his wife that he is directly influenced by her action usually in an opposite way. 🤣
Jocofranc
It Is Also The Brightest Star Of The The Constalellation Of Piscis Austrinus.....
who was the first person to get to the planet
Isaac
can anyone tell me daily rotation of the sun in tokyo
tokyo has it's own personal sun
Tracy
can you send me any pictures of the tokyo sun
Liridona
sure! ig?
Tracy
here can u?
Liridona
no it wont let me sadly
Tracy
or
Liridona
snapchat
Liridona
i dont have snapchat 😰
Tracy
okay ig
Liridona
my ig is fatwigga37 if you'd like to see :)
Tracy
Can we use SI units in the equation of Kepler's third law?
can u tell the equation pls
sasmita
how does religion enters to this topic when god created this world
Sakira
How Do You Know A God Created Our Planet?
Sakira
u must the bible
Sakira
How Do You That Book Is Authentic? And I Have Read The Bible, The Koran, The Torah And The Urantia.....
The law is T^2 is proportional to R^3 where t is planet's time period and r is average of semi major axis and semi minor axis. Also,don't turn this place into a religious warzone. We already have idiots fighting about religion.
priyanshu
If I Had A Book That Said Insects Created The Universe, Would That Make It Fact?
Have You Ever Heard Of The Council Of Nicaea?
Through Out History Mankind Has Worshipped Over 5000 Different Gods, How Do You Know Christ Is The True God?
God Is A Hypothesis..... The Definition Of Faith Is Belief Without Proof.....
Thank You Prianshu Roy, This Is A Forum For Science Not Archaic Stories Written By Sheep Herders, Well Said.....
Hebrew 13:1
onome
P2 = a3
So You Quote A Bible Verse, Now What?
Science Discourse Nothing Else.....
god is real he's not just a wise guess
Sakira
god bless you
Sakira
u know what,u are not here if god werent there!
Sakira
Science Discourse, Nothing Else.....
Thier Are Many Religious Sites You Can Go To, To Discuss God.....
hahahaha
Sakira
Have A Great Day.....
night time here
Sakira
Look Up The Definition Of Day, Instead Of Trying To Look Witty, Again Have A Great Day.....
😈😈😈
Sakira
such an socratic person?
Sakira
What Was Your Intention In Stating "Night Time Here" ?
please don't fight over silly stuffs!
Romancho
tangina mo
Sakira
No I Don't Believe A God Exist, But I Will Fight For Your Right To Worship Any God You Wish.....
no fighting
Sakira
But This Venue Is For Science Discourse.....
i know!
Sakira
No Fighting, Just Discussion.....
yes Naiyu, we have to use SI unit in the equation for the Kepler's every laws
Thanks.
Naiyu
wow
Kenneth
what's the scene of voyager 1,did we get any information through it
we are getting a lot of info yet more to be received check official mission report from the officials site ....
Ganeshan
what are the best astronomy books?
what is the parallel space?
neehar
how to measure the brightness of a star in w\m^2
it's based on the percentage of helium I think
neehar
ok TQ😊
Aarushi
it's based planet colour and brightness which called lumiosity
gdjm
Are there planets that has the same characteristics as earth.
yes ofcourse there are earth like planets but they aren't completely like earth.still scientists have a hope of life existence in there.
Aarushi
yeah of course example is Mars but they only discover water at mars
neehar
there's a much possibility of presence of earth like planets in the universe if they were present at goldilock zones
Jashwanth
what are goldilock zones?
Aarushi
why yes there are planets just like earth out there somewhere we know that much for sure given the number of planets in the galaxy, as a matter of fact, one of Jupiter moons officially named "gamamede" is very much like earth in size and characteristics
Hunter
How to become an astronomy
astronomer*
Emilya
Yes
Aakarsh
Astronomer
Aakarsh
yes i Also want to know the answer
Mehar
How to become?
Aakarsh
Me too
Romancho
By hard study
Zulker
Try to keep all the basics of science subjects and also English
Zulker
Ya i know that I will do hard work but
Aakarsh
I have always found astronomy fascinating, but my first love is philosophy.
GARY
I wanna become astromer as neel armstrang
Aakarsh
that's an astronaut
Emilya
Neil Armstrong
antman
what is your name who are you where are you why are you there
GARY
Neil Armstrong was an astronaut. You first work is to know the meaning of astrophysicist, astronomer, astronaut, astrologer and to find the work of the individual. And the most important thing is to be good in English. Because u have done some mistakes while doing chat with me like :an astronomer
Zulker
sorry I'm talking to somebody else someplace else on the internet
GARY
The heading will be "How to become an astronomer"
Zulker
jus be yourself and follow your passion and I think there is no need to copy anyone
Aarushi
hey it's simple yaar, it's based on your curiosity
neehar
what is the length of Earth
The Earth is not a perfect sphere, however it's roughly 25,000 miles, or 131.5 million feet, or 1.6 Billion inches. In the Metric system its HUGE!
Jocofranc
nyo
But can I also know and calculate the whole weight of earth includeing flora, funa,water on earth even air's weight.Depending on super compruter, I think it can be.For the very detail in the Metric System.Such as kilogram and pound.
nyo
Earth is about 6 Sextillion metric tons check out formula at ***science.howstuffworks.com/environmental/earth/geophysics/planet-earth-weigh.htm
Jocofranc
thank again Sr.I wanna ask another question if you don't mind.The earth had 4.5billion years age old.My question is from fire ball to today more and more stable geology was how happen.Please answer me starting of life on this planet and how many era are there and the earth history.
nyo
My friend you have asked a question(s) that scientists struggle with. There is no short cut...the information is lenghty. Here is an additional site for you. It is a good place to start. ***newscientist.com/article/dn17453-timeline-the-evolution-of-life/
Jocofranc
Sr,your web site is very useful to me.And another question is how gene or DNA transfer from parent to sibling.how we know the first DNA of our first human from arfarica.
nyo
Jocofranc
If speed is so many thousand time of light and start to travel from one point,how speed will return to it starting point even in straight line back.Will time and energy be limit it?Can it be posible.Please let me explain Sr.
nyo
hey neo ur curiosity is great, where r u from?
neehar
in physics actully no but thory make possible
gdjm
earth is about 13,000 kilometers across
Hunter
there is aliens or parallel universe
There may be both who knows
Debabrata
It would be quite surprising to me to learn that there is no aliens in our very own galaxy. The size of our galaxy alone seems to favour life. There's so many reasons why we haven't made contact but as our technology grows we will undoubtedly find answers. I also think that it's possible that ...
Jocofranc
But I don't think that that alien species might be developed.... Because if they were developed or advanced than us then they must have located us first and might have even contacted us
Debabrata
many other universes exist. I don't think that they would be parallel universes in the purest sense of the word. Only speculations on my part. We simply dont know with certainty.
Jocofranc
Hi Debabrata; You may be right. It's hard to say with certainty. An ugly truth (guess really) is that Tellurian are simply not interesting. We are not all that!
Jocofranc
Yeah Jocofranc you are also right about parallel universe. Who knows what lies ahead.
Debabrata
the parallel universe theory is something secondary but first let's focus on the nearby objects like titan which shows great hope
Aarushi
I read it before about aliens, but I have to research on it
neehar
yeah of course
neehar
What about XTs... Exo-Tellurians. Ancient people who could have obtain a spurt of technology and left home. Progression of men r not always linear but sometime cyclic. Civilization comes and goes. Geo-upheaval can easily erase any evidence. Our bros r out there. (have fun 😁)
Jocofranc
sir jocofranc I think u didn't listen about aliens who send a message to our space research organization.
neehar
what is inside Jupiter how it will rain there
interesting question!
Mahesh
would love to learn about it 😃
Morrie
jupiter is a gas gaint so you can't walk on the surface like here on earth, but there is a solid core.
Yannick
The latest term being used is a 'fuzzy core'. An inbetween of solid and liquid. Check ***sciencemag.org/news/2019/08
Jocofranc
I think it based on the nature of the source in Jupiter
neehar
Scientists believe that onJupiter and Saturn, it rains diamonds. New atmospheric data for the gas giants indicates that carbon is abundant in its dazzling crystal form, the BBC reports. Lightning storms turn methane into soot which hardens into chunks of graphite and then diamond as it falls.
gdjm
Where is a moon HOW MANY KILLOMETER FAR FROM EARTH
On Average 383,000 Kilometers, Between Perigee And Apogee.....
386,000 km
neehar
3.6×10^5 km
gdjm