in this video we're gonna talk about how

to balance nuclear equations so in this

example problem we have an isotope of

carbon carbon-14 undergoing beta decay

which means that it's emit an a beta

particle or an electron what is the

missing element in this reaction in

order to do that we need to make sure

that this reaction is completely

balanced there's two numbers of

interests the six represents the atomic

number of the element carbon which is

equal to the number of protons in this

particular element which is the same as

the charge on the nucleus the top number

the 14 represents the mass number of the

element it's the sum of the number of

protons and neutrons so in this element

in carbon 14 that isotope has 6 protons

8 neutrons 14 minus 6 is 8 now in order

to balance a nuclear equation we need to

make sure that the mass is the same on

both sides and also the total nuclear

charge has to be the same so right now

this is zero which means that we're

missing the 14 because we need a sum of

14 on the right and 14 on the left now

on the left side in the total nuclear

charge is 6 on the right side it's a

negative 1 so negative 1 plus what

number is 6 now what you could do is you

can write an equation you can say 6 is

equal to negative 1 plus some missing

number which we can call X and then do

some algebra in order to get X by itself

we need to add 1 to both sides so X is 7

so now that we've identified the missin

atomic number we need to identify the

element and we need to use the periodic

table to get the job done so the mass

numbers can vary for different elements

or even for the same element however the

atomic number always identifies the

element so using the periodic table what

element has an atomic number of seven

there's only one and this is nitrogen so

that's how you can identify the missing

element it's by looking at the atomic

number and now the equation is balanced

we can see that the mass numbers are the

same on both sides it's 14 on both sides

and the nuclear charge is also the same

it's 6 on the left and it's a total of 6

on the right negative 1 plus 7 is 6 so

that's how you can balance a nuclear

equation now let's get rid of that

here's another example nitrogen 14 is

bombarded with neutrons in the upper

atmosphere and as a result it produces

hydrogen and some missing element and

what is the missing element that we need

to put there to balance this nuclear

equation and go ahead and try this

problem feel free to pause the video if

you want to

so first let's determine well let's

write an equation starting with the mass

numbers so let's put M for mass numbers

so on the left side we have 14 plus 1

and that equals 2 on the right side 1

plus some number let's call this Y and

let's call this X and we'll call the

element actually let's use a for this

because that's let's make this M I'm

going through different letters here M

is for mass number Z is for atomic

number I will say a is the element

so this is gonna be one plus M so we

have fourteen plus one is equal to one

plus M now let's solve for M note that

if we subtract one from both sides these

two will cancel and we'll get that M is

equal to 14 so let's replace M with phat

now let's calculate the atomic number Z

so on the left if we focus on the bottom

numbers we have seven plus zero and

that's equal to one plus C so trying to

get Z by itself if we subtract both

sides by one we can see that Z is six

and the element with an atomic number of

six we know this to be carbon so when

nitrogen 14 in the other atmosphere is

bombarded by neutrons in space it

produces hydrogen and it regenerates the

carbon-14 isotope now let's work on some

more examples so next we have thorium

230

this particular element undergoes alpha

decay so now a particle is basically a

helium nucleus go ahead and identify the

missing element calculate the mass and

the atomic number of the missing element

and then identify that element so once

again let's write an equation so we have

230 is equal to 4 plus M looking at the

numbers on top so to solve for M we're

going to subtract both sides by 4 thus

the mass of the missing element is 226

now let's use the numbers on the bottom

that is the nuclear charge or the atomic

numbers so 90 is equal to 2 plus C

subtracting both sides by 2 we get that

Z is equal to 88 so now let's get rid of

this

so our mission element has a mass of 226

and an atomic number of 88

so what element according to the

periodic table has an atomic number of

88 this element is our a a radium so

that's how we can balance this

particular nucleation and at the same

time identify the missing element here's

another example mercury 201 undergoes

electron capture that is where the

nucleus captures an inner core electron

and it produces a gamma particle plus a

misson element what is the missing

element so just by looking at this we

can see that M is going to be 201

because here we have a zero so we know

that the mass of the missing element is

201 and Z we can clearly see that ze is

the sum of these numbers because the

zero is not going to change anything so

80 plus the negative 1 is 79 so the

missing element has a mass of 201 an

atomic number of 79 and now using the

periodic table we can identify what

element has an atomic number of 79 and

this is gold so when mercury 201

undergoes electron capture it turns into

gold 201 what about this example

aluminum 27 is bombarded with an alpha

particle

and it produces a neutron and a missing

element go ahead and work on that

example so starting with the numbers on

top we see that 27 plus 4 is equal to 1

plus M so add in 27 and 4 we get 31 and

then subtracting 1 from both sides we

can see that M is 30 in this example now

focusing on the numbers on the bottom we

have 13 plus 2 is equal to 0 plus a Z 0

plus Z is show Z 13 plus 2 is 15 so the

atomic number is 15 so we have a mass of

30 an atomic number 15 and the element

that corresponds to a nuclear charge of

15 is phosphorus so that's the missing

element in this example now let's work

on one more practice problem let's say

we have uranium 238 and it's bombarded

with carbon atoms and in this process it

generates 6 neutron particles plus the

missing element what is the missing

element in this case so let's put em Z

and a so let's start by calculating them

on the left side we have 238 plus 12 on

the right side we have 6 times 1 so

don't forget to multiply the 1 by 6 and

then let's do the algebra 238 plus 12 is

250 and then if we subtract 250 by 6 we

get 244 so that's the mass number in

this example now focusing on the numbers

on the bottom we have 92 plus 6 is equal

to this is 6 times 0 so you could ignore

that and then plus Z so 92 plus 6 is 98

so we have a mass number of 244 an

atomic number of 98

so what none limit has an atomic number

of 98

this element is californium CF so that's

it for this video now you know how to

balance in nuclear equations thanks for

watching