Understanding Beta Decay: A Comprehensive Overview

good morning today our primary objective will be to review beta decay

specifically we'll try to understand what those symbols mean and we'll come to understand that

radiation is emitted during a beta decay and that a new element or atom is formed ultimately beta decay happens because a

nucleus is unstable so the question we'll be answering is when is the nucleus of an atom stable or

unstable we'll also be looking at common word problems

example one a beta decay process occurs where a positron is created

solve for x for the following nuclear reaction we'll also look at example two

and example three so when is the nucleus of an atom stable or unstable

well here's a nucleus and focusing on the nucleus and counting the number of neutrons and protons

we have six protons and six neutrons now recall that protons have a positive

charge as a result since there are only protons within the

nucleus they will repel each other this is referred to as an electrostatic

force so what keeps a nucleus together well clearly it's not the electrostatic

force a nucleus only has protons remember that the neutrons do not have a charge

and the protons will be repelling each other so there must be another force within a

nucleus that keeps it together that other force is called the strong nuclear force

or just a strong force both the neutrons and the protons experience a strong force

neutrons attract neutrons with this force protons attract protons and in addition protons attract neutrons and

vice versa this force acts at short distances and really only within the nucleus

so when is the nucleus of the atom stable or unstable well there's two factors to consider

the ratio of the number of neutrons to the number of protons and the size of the nucleus helium which

is small compared to uranium which is much larger so we're going to use this graph to

think about this question on the x-axis we have the number of protons

on the y-axis the number of neutrons and i've plotted a line there which represents a one-to-one ratio of

neutrons to protons so we'll look at some very general trends but remember there's always some

outliers so we'll begin with small atoms usually

when the number of neutrons is equal to the number of protons the atom is stable

so for example carbon 12 which is six neutrons and six protons that stable

but carbon 14 is unstable eight neutrons compared to six protons and carbon 10 is also unstable

four neutrons in comparison to six protons sodium 23

with 12 neutrons and 11 protons that is considered stable but sodium 24 with an extra neutron is

unstable magnesium 24 magnesium 25 and magnesium 26

is all considered stable so for larger atoms in general the number of neutrons is greater than the

number of protons for the atom to be considered stable nickel 58 with 30 neutrons compared to

28 protons is stable but nickel 63 with 35 neutrons is unstable

krypton 84 is considered to be stable with 48 neutrons compared to 36 protons but krypton 85 is considered to be

unstable with an extra neutron a nucleus that is unstable will decay which means that the number of protons

and neutrons will change during this decay energy is emitted by the nucleus and that's why it's called a

radioactive decay the energy is emitted in the form of radiation so now let's focus on beta decay

during the decay of an unstable necklace a beta particle is emitted and there are two types of beta decay

beta minus and beta positive or beta plus beta minus an electron is emitted

or ejected and for a beta plus decay a positron is ejected or emitted

so now let's focus specifically on a beta minus decay within the nucleus a neutron transforms

into a proton emitting from the nucleus an electron which is a beta-minus particle

an anti-neutrino and radiation sometimes this is also referred to as a negative beta decay

so examples of beta minus decay well let's focus on our nucleus and counting we have six protons and

eight neutrons this decays to form seven protons and seven

neutrons notice that a neutron has been transformed into

a proton during all beta decays charge has to be conserved

that means that the total charge before the decay has to equal the total charge after the

decay now if we look right now we know that neutrons do not have any charge so

before the decay we have six protons a charge of plus six

after the k we have seven protons so right now charge seems to not be conserved as six

is not equal to 7. however this is not the complete process we have a neutron

transforming into a proton but in addition when this occurs an electron is emitted or ejected by the

nucleus now going back to this equation and recalling that we now have to

consider the charge of an electron and that charge is negative one now charge is conserved as seven plus

negative one is equal to six so this is the overall picture of any beta minus decay

we have the conversion of a neutron to a proton an electron which is the beta particle

is emitted radiation is also

emitted by the nucleus and we have this particle that we haven't discussed yet

it's also emitted this particle is called an anti-neutrino what's important

to know about this particle is that it has no mass and no charge looking at the nucleus

we can write that this nucleus is carbon 14 6. the 14 is the atomic mass number it

comes from adding the number of neutrons with the number of protons and six is the atomic number

the number of protons this nucleus can be represented by nitrogen fourteen seven fourteen comes

from seven plus seven so we can use this equation to represent what we just described

this equation may also be written like this where we include the mass

and the charge the electron mass is considered to be zero as it's tiny in comparison to the mass

of a neutron or a proton the mass of electron that is and this refers to the charge electron

you may also see this equation written in this form as well notice that 14 on one side is equal to

14 on the other side notice that the atomic mass number does not change

14 equals 14 plus zero plus zero reviewing this row of numbers we see that charge is conserved

meaning six equals seven plus negative one plus zero

comparing alpha particles to beta particles alpha particles usually cannot pass

through paper however beta particles can pass through paper

usually however beta particles cannot pass through aluminum foil

turning our attention to beta plus decay within the nucleus a proton transforms into a neutron

emitting from the nucleus a positron which is called a beta plus particle a neutrino and radiation

a positron has the same mass as an electron however it has a positive charge

positron is said to be the antimatter counterpart of the electron sometimes a beta plus decay is also

called a positive beta decay so let's look at one example of a beta plus decay

focusing on nucleus we have six protons and four neutrons a decay takes place

and we have a new nucleus notice that a proton has been transformed

into a neutron now we have five protons and five neutrons

and this is the complete picture of what will happen during this decay we have a proton being converted into a

neutron we have a positron being ejected or emitted by the nucleus

represented by e plus radiation and we have this particle here

this particle is called a neutrino it has no mass and no charge reviewing this nucleus we can write it

as carbon 10 6. and this can be written as boron 10 5. the beta decay can be represented with

this equation or with this equation here where the zero is written there because

we consider the mass of the positron to be very small it's extremely small in comparison to the

mass of the neutron and proton and the one represents the charge of the positron

and that's identical to the charge of a proton you may also see this equation written

with the symbol beta notice once again this row here 10 equals 10 plus zero plus zero

and notice this particular row here six equals five plus one plus zero you may come across the term parent and

daughter the daughter nucleus is what results after the parent nucleus has undergone a decay

so now to summarize what we've learned the daughter nucleus and the paranucleus have the exact same

sum of neutrons and protons that does not change during a decay another way of saying that is that the

daughter nucleus has the same atomic mass number as the parent nucleus and yet another way of saying the same

thing is that the total number of nucleons remains unchanged

a nucleon is a proton or a neutron only the atomic number changes during a beta decay

going back to this graph let's say we're on this side of the graph in other words we have an atom

and when we plot the atom's number of protons compared to the number of neutrons it's somewhere in the region

that i've highlighted there typically when this

takes place that particle or nucleus

will undergo a beta plus decay so for example carbon 10.

carbon 10 has six protons and four neutrons so if we plot that data point it'll be approximately that area there

where i've pointed with the arrow and that will undergo a beta plus decay

when it goes through a beta plus decay it ends up having five neutrons and five protons

so now if we look at the region i just highlighted and if we have a nucleus that has a

number of protons and number of neutrons that falls in that region typically

it'll undergo a beta minus decay for example carbon 14 which has eight neutrons and six protons

the arrow points to that data point which is approximately plotted there and this will undergo a beta minus decay

the resulting product being seven neutrons and seven protons

being nitrogen now on to our secondary objective to review those three examples

example one a beta decay process occurs where a positron is created solve for x

please pause the video now all right i hope you've tried this question

i'm just going to rewrite this to include the numbers for the positron positron having mass number of zero and

a charge of one and now we're just going to focus on that row

six equals x plus one or x equals five remember

during a beta decay a beta plus decay a neutrino is always created as well

so that should be included in the equation example two

uranium-237 undergoes a beta decay process when electron is emitted a beta minus decay solve for x for the

following nuclear reaction once again when this decay takes place you should

include whether it's a neutrino or an anti-neutrino in this case for a beta minus decay it is an anti-neutrino

please pause the video now okay i hope you've tried this question for the electron i'm just going to

rewrite it with a mass number of zero and a charge of negative one

now we're going to walk through the math 92 equals x plus negative 1 or x equals 93.

finally example 3. sodium 22 undergoes a beta decay process where a positron is emitted beta plus

decay solve for x for the nuclear reaction please pause the video

okay i hope you've tried this question once again it's important to note that we should add that a neutrino is also

created during this decay and going through the math x equals ten plus one

why is it one well it's one because the positron has a charge of one or x equals eleven

so in conclusion i hope you've enjoyed this review of a beta decay

have a great day bye