Thread: k capture

hello everyone. my doubt is pertaining to k-capture. i hope you all know it. if not, in some higher nuclides the nucleus may capture the k shell electron and the proton present inside the nucleus and the electron captured they combine to form a neutron.

to make things much simple look at this example
eg: barium--(by k capture)-------> cesium + x-ray
so here

proton + electron------------> neutron

but when i took the conservation of mass in to account the mass i obtained by adding the masses of proton and electron is slightly less than the neutron

so what i thought was may be there is some another particle involved in the above reaction(i,e p + e = n)
let me tell you the values also i've obtained when i took the difference between neutron mass and the mass which i've obtained on adding up the masses of proton and electron
1) in kgs it is 0.0014 * 10^-27
2)in amu it is 0.00086

IIRC a neutrino is also emitted but this doesn't solve your problem. You are aware that mass and energy are just manifestations of the same thing? This is not really my area but I would put the slight mass difference down to changes in nuclear binding energy that arise from having a neutron bound in the nucleus where there was previously a proton.

well i know that a neutrino is emitted but i am studying 11th now and in one of my reference books in the example of k capture they haven't mentioned any neutrino ejecting or emitting. i know that the book is wrong and do you have any idea on what type of neutrino is emitted?

Presumably it is an electron neutrino. As for your book being wrong, this is a common problem with school text books, they oversimplify things (in some cases to the point of incorrectness) to make sure the fundamentals are understood without confusing students with extra variables they don't need to know about yet. I'm guessing this is why they haven't mentioned neutrinos (or the change in binding energy as a possible answer I mentioned in my first post).

bro thanks for considering one possibility. i,e the electron neutrino one. but still my doubt isn't cleared.

how proton plus electron is a neutron? just answer for this

Originally Posted by dheeraj

how proton plus electron is a neutron? just answer for this

I don't know for sure, but I assume the weak interaction causes an up quark to turn into a down quark.

Proton = uud. Turn one of the ups into a down and you get udd = neutron. (Plus a neutrino to conserve lepton number and spin.)

Start here:

Electron capture - Wikipedia, the free encyclopedia

proton + electron gives a neutron + an electron neutrino.

The electron neutrino is needed to ensure conservation of energy, spin, momentum and angular momentum.

You need to bear in mind that protons and neutrons are not elementary particles but are composed of quarks. Electron capture and beta decay are governed by the "Weak Interaction" through which a quark in a proton which captures an electron can change "flavour", the result of this "flavour change" is the conversion of a neutron to a proton (or vice versa). (This isn't my area of expertise but that's my understanding of it).

if you are saying the right thing then like you may check in any websites regarding the mass of an electron neutrino is said that "close to zero" but using this equation can't we get the exact mass of an electron neutrino? by using conservation of mass. isn't it obvious? and moreover i got the mass of an electron neutrino as 0.00086 amu which is more than the mass of electron(0.00054amu)
i,e

n0 → p+ + e− + ν0
e

Originally Posted by dheeraj

if you are saying the right thing then like you may check in any websites regarding the mass of an electron neutrino is said that "close to zero" but using this equation can't we get the exact mass of an electron neutrino? by using conservation of mass. isn't it obvious?

I think the problem is that some of the missing mass-energy goes into the mass of the neutrino and some goes into its kinetic energy. And the velocity isn't easy to measure.

But it is not just mass you have to consider, it is mass-energy that is conserved not mass (remember E=mc²) so any mass discrepancy you have found MUST be accounted for by a change in energy (either emitted as kinetic energy of the neutrino as a photon or a change in the binding energy of the nucleus as I said above). In nuclear (and quantum) processes you cannot treat mass and energy in isolation as you can in macroscopic systems where the mass changes are many orders of magnitude greater than the energy changes.

yeah you are right on the possibility which you've considered that some of the mass is going off from neutrino and that mass is forming into a new particle that is our electron neutron and if only some( < 0.00086 amu ) amount of it's(neutron's) mass is going off to the neutrino the conservation of mass isn't valid then. get it?

Originally Posted by dheeraj

yeah you are right on the possibility which you've considered that some of the mass is going off from neutrino and that mass is forming into a new particle that is our electron neutron and if only some( < 0.00086 amu ) amount of it's(neutron's) mass is going off to the neutrino the conservation of mass isn't valid then. get it?

Correct. Conservation of mass is not valid (it is a useful approximation). It is conservation of mass and energy.

well all of a sudden why are you saying that conservation of mass isn't valid?

Originally Posted by dheeraj

well all of a sudden why are you saying that conservation of mass isn't valid?

It is only valid in specific circumstances (closed systems, mainly). More generally, you have to consider mass and energy.

again all of a sudden where does energy come from? and isn't it a closed system? the reaction is happening inside the nucleus. isn't it?

Originally Posted by dheeraj

well all of a sudden why are you saying that conservation of mass isn't valid?

Nothing sudden about it, did you read what I said in post 2? The fact you have to take energy as well as mass into account is clearly stated and I expanded upon it in post #10. As Strange has said, conservation of mass is only an approximation, the real conserved quantity is (mass + energy) not mass.

well bro to make things much simpler to you'll see in this reaction
n0 → p+ + e− + ν0
e where ​do you see energy?

Originally Posted by dheeraj

again all of a sudden where does energy come from? and isn't it a closed system? the reaction is happening inside the nucleus. isn't it?

No. The electron comes from outside, with some amount of (unknown) kinetic energy. The neutrino leaves with some (unknown) amount of kinetic energy. And, as stated, the vast majority of the mass of an atom comes from the binding energy in the nucleons.

Originally Posted by dheeraj

well bro to make things much simpler to you'll see in this reaction
n0 → p+ + e− + ν0
e where ​do you see energy?

To keep it simple everywhere. This does not happen in isolation, there is the binding energy of the nucleus, the "mass" of all the particles can be considered as energy (E=mc2 again), the particles are moving and so have kinetic energy, there is a x-ray photon emitted as well which you seem to have ignored since post 1, all of these contain or have energy that must be taken into account. I don't know how to explain it any simpler.

i know that a x ray is emitted and i was just clearing my doubt or i was having doubt in the nuclear wise side of the example so i neglected the x ray

electron comes outside? well i don't see any electron coming outside in the very example i've given on k capture. do you?

But this is what we are saying, you CANNOT neglect the X-ray or anything else that has energy if you are trying to show conservation of mass-energy. They have energy, they need to be taken into account. One more time it is not mass that is conserved but mass-energy. Convert all mass and energy in the system to the same system of units (i.e. everything in joules or kilograms -- E=mc2 again) and it is this sum of mass and energy that is conserved. Your doubts seem to be due to you not understanding the equivelance of mass and energy.

Originally Posted by dheeraj

electron comes outside? well i don't see any electron coming outside in the very example i've given on k capture. do you?

In post #17 your example is beta decay not electron capture, this is what Strange is referring to.

okay i get your point now so acc to you
barium -----(k capture)----------> cesium + x ray + electron neutrino. correct me if am wrong here.
so in the above reaction there has to be some mass left out in the lhs or rhs sides so that the mass which is left out is turning into the x ray am i right?
if so like i said to conserve mass a part of mass(pproxly 0.00086 amu ) is going off the neutron then how it is called neutron? like if i ask you what is the subatomic particle of mass 1.67493 * 10^-27 kg? you'll say neutron without any hesitation. in the same way if i ask you if 0.0014 * 10^-27 kg's of mass is removed from the neutron's mass then also would you say me that would be neutron? i don't think you will say that will you?

what? well what do you think happens in k capture or electron capture? bro this is what happens in electron capture too

You are sort of getting it but it is not only the X-ray.

Mass and energy on LHS.

Mass of Ba nucleus. + Kinetic/potential/binding energy of Ba nucleus + Mass of electron + kinetic/potential energy of electron

Mass and energy on RHS

Mass of Cs nucleus +kinetic/potential/binding energy of Cs nucleus + energy of X-ray + mass of neutrino + kinetic/potential energy of neutrino

After that I'm out, I've explained it as simply as I can, if you still don't get it I'll leave it for someone else to try and explain in terms you can understamd.

Originally Posted by dheeraj

what? well what do you think happens in k capture or electron capture? bro this is what happens in electron capture too

No, not at all, beta decay is the conversion of a neutron into a proton and electron, K-capture is the conversion of a proton and an electron into a neutron... I'll leave someone else to try and get it through to you...

check this out once phdemon Electron Capture Definition - Definition of Electron Capture

We should consider the mass of Neutrino wich is less than 2.2 eV.What about it? o.O

as of now you've said that beta decay is the conversion of a neutron into a proton and electron so

neutron=proton + electron right?
but conservation of mass isn't valid here too.

which neutrino's mass exactly? bharath

It's of Electron Neutrino.

Originally Posted by dheeraj

check this out once phdemon Electron Capture Definition - Definition of Electron Capture

Which is what I've been saying all along. Nothing there contradicts anything I have said (and no it is not the same as your example in post #17. Now I've wasted enough time on this thread, you seem to be having trouble understanding what I'm trying to explain to you so I won't waste any more.

any idea about 1 ev = how much in kg's , gm's, amu?

It's electron volt.And it is Mass-energy equivalent.Hence,it is considered as unit of mass,Dheeraj..!

i know it's an electron volt. and i also do know that it is a unit of mass, and here you go bharath... Convert kg to electronvolt - Conversion of Measurement Units

Originally Posted by dheeraj

electron comes outside? well i don't see any electron coming outside in the very example i've given on k capture. do you?

Yes, you are right in this instance, I had forgotten you were talking about k capture. I was thinking of the more general case of weak interactions.

Originally Posted by dheeraj

i know it's an electron volt. and i also do know that it is a unit of mass

Actually, eV is a unit of energy. It needs to be divided by c² to convert it to mass. (Although, I think people are sometimes a bit sloppy and just use eV to refer to mass.)