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Specific Charge!!

I don't get it at all. Some answers seem to be correct and others don't, even with the same working out.

Q) An isotope of Uranium has 92 protons and 143 neutrons. Calculate its specific charge in Ckg1Ckg^{-1}

C=92×1.6×1019235×1.67×1027C=\frac{92 \times 1.6 \times 10^{-19}}{235 \times 1.67 \times 10^{-27}}

C=3.8×107Ckg1C=3.8 \times10^7Ckg^{-1}

Ok so that's correct.

However, if I apply the exact same working S.C.=chargemassS.C.=\frac{charge}{mass} it's not correct. For example,

Q) Mg1224Mg_{12}^{24}

charge = 24×1.60×1019=3.84×101824 \times 1.60 \times 10^{-19}=3.84 \times 10^{-18}
mass = 24×1.67×1027=4×102624 \times 1.67 \times 10^{-27}=4 \times 10^{-26}

S.C.=3.84×10184×1026=9.6×106Ckg1\frac{3.84 \times 10^{-18}}{4 \times 10^{-26}}=9.6 \times 10^6Ckg^{-1}

This is wrong. The book states the s.c. is 8.04×106Ckg18.04 \times10^6Ckg^{-1}

It also states the charge is 3.2×10193.2 \times 10^{-19} not 3.84×10183.84 \times 10^{-18}. Why is this?

To calculate the charge (not specific charge) of a particle, I am multiplying the proton number by 1.6×10191.6 \times 10^{-19}, since neutrons have no charge.

To calculate the mass, I am multiplying the nucleon number (protons and neutrons) by 1.67×10271.67 \times 10^{-27} yet this isn't correct.

What am I doing wrong here?

Reply 1

Firstly,



shows an atomic mass of 24 (neutrons + protons)
shows proton number 12

Secondly, it is a magnesium ion (charge +2) :eek3:

Thirdly, the book uses really accurate values of avogadro's thingy and elementary charge in addition to crazy rounding.



So using:

S.C=charge/massS.C = charge/mass

Charge=2×1.60×1019[br]=3.2×1019Charge = 2\times 1.60 \times 10^{-19}[br]\\\\=3.2\times 10^{-19}

Mass=24×1.67×1027Mass = 24\times 1.67 \times 10^{-27} Sorry, typo before.

S.C=8.036×106Ckg1S.C = 8.036\times 10^6 Ckg^{-1} or 8.04×106Ckg1 8.04\times 10^6 Ckg^{-1} to 1dp

Reply 2

Chelle-belle
Firstly,



shows an atomic mass of 24 (neutrons + protons)
shows proton number 12

Secondly, it is a magnesium ion (charge +2) :eek3:

Thirdly, the book uses really accurate values of 1/avogadro and elementary charge in addition to crazy rounding.



So using:

S.C=charge/massS.C = charge/mass

Charge=2×1.60×1019[br]=3.2×1019Charge = 2\times 1.60 \times 10^{-19}[br]\\\\=3.2\times 10^{-19}

Mass=24×6.02×1027Mass = 24\times 6.02 \times 10^{-27}

S.C=8.036×106Ckg1S.C = 8.036\times 10^6 Ckg^{-1} or 8.04×106Ckg1 8.04\times 10^6 Ckg^{-1} to 1dp
]

ok thanks but why do you times it by 2, not the no. of protons?

how would you calculate Cu2963Cu_{29}^{63} when it loses two electrons?

Are there any rules which makes this easier? Is there a different method for calculating the SC of an ion to a charged particle?

A little help please :smile:

Reply 3

I think maybe you are stuck on the concept of ions and charge.
An ion is a charged particle.

You get an ion when number of electrons is not equal to the number of protons (hence charged particle.) So, referring to our friend the periodic table, we can see that Magnesium is in Group 2. If you know about what each part of the periodic table means, you will know that the Group number (ie. vertical columns, Groups 1 to 8) will refer to the number of electrons on the outer shell.



Elements like to have 8 electrons on their outer shells.


Look at the outermost shell. What is easier? Gaining 6 electrons, or only losing 2? The answer is losing 2.

We know that electrons have a negative charge, so if you lose 2 electrons, you end up with positive charge (it's like two negatives together in maths make a plus.)

What this means is that a Magnesium ion will probably have a charge of +2.

A magnesium atom:

(Atomic mass 24, proton number 12.)

You can only have a specific charge of a particle with charge! (Makes sense, no?)

12×1.6×101912\times 1.6\times 10^{-19}.

This is essentially saying the atom has a "charge" (it's not the charge in amps as we know yet) of +12 (this is wrong. The element has no charge normally, but the sake of understanding...), and you're multiplying that by elementary charge (1.6... to convert to coulombs).

So when you have the ion, the "charge" is replaced by +2, so you multiply that by elementary charge instead.

Does this help at all?

Reply 4

Justin1265
]
how would you calculate Cu2963Cu_{29}^{63} when it loses two electrons?
Are there any rules which makes this easier? Is there a different method for calculating the SC of an ion to a charged particle?

I highly suggest seeking help from your teachers about this to get a good grade by the way as some fundamental concepts are being misunderstood! In time, you will probably be okay, but for now it is best to clear up any confusion as well as you can.

Reiterating my point before: You can only calculate the SC of charged particles (such as ions).


Before I forget, I am a little confused on the question where your working out was:



Is that the full question with the exact wording? Are you missing any information out again like the vital information that it was a Magnesium ion? I will have another look later.

Edit: I think you are also getting confused between finding the S.C of an ion (this is where electrons have been taken into account) and the S.C of a nucleus (where you ignore electrons, and simply find out the charge of protons in the nucleus.)

If you understood what I was saying before, technically you should be fine with working out



Spoiler

Reply 5

Original post by Chelle-belle


So using:

S.C=charge/massS.C = charge/mass

Charge=2×1.60×1019[br]=3.2×1019Charge = 2\times 1.60 \times 10^{-19}[br]\\\\=3.2\times 10^{-19}

Mass=24×1.67×1027Mass = 24\times 1.67 \times 10^{-27} Sorry, typo before.

S.C=8.036×106Ckg1S.C = 8.036\times 10^6 Ckg^{-1} or 8.04×106Ckg1 8.04\times 10^6 Ckg^{-1} to 1dp


Hi there, wheb i try this calculation it gives 7.98x10^6. What would the correct calculation be to get 8.04x10^6?

Reply 6

Original post by Justin1265
I don't get it at all. Some answers seem to be correct and others don't, even with the same working out.
Q) An isotope of Uranium has 92 protons and 143 neutrons. Calculate its specific charge in Ckg1Ckg^{-1}
C=92×1.6×1019235×1.67×1027C=\frac{92 \times 1.6 \times 10^{-19}}{235 \times 1.67 \times 10^{-27}}
C=3.8×107Ckg1C=3.8 \times10^7Ckg^{-1}
Ok so that's correct.
However, if I apply the exact same working S.C.=chargemassS.C.=\frac{charge}{mass} it's not correct. For example,
Q) Mg1224Mg_{12}^{24}
charge = 24×1.60×1019=3.84×101824 \times 1.60 \times 10^{-19}=3.84 \times 10^{-18}
mass = 24×1.67×1027=4×102624 \times 1.67 \times 10^{-27}=4 \times 10^{-26}
S.C.=3.84×10184×1026=9.6×106Ckg1\frac{3.84 \times 10^{-18}}{4 \times 10^{-26}}=9.6 \times 10^6Ckg^{-1}
This is wrong. The book states the s.c. is 8.04×106Ckg18.04 \times10^6Ckg^{-1}
It also states the charge is 3.2×10193.2 \times 10^{-19} not 3.84×10183.84 \times 10^{-18}. Why is this?
To calculate the charge (not specific charge) of a particle, I am multiplying the proton number by 1.6×10191.6 \times 10^{-19}, since neutrons have no charge.
To calculate the mass, I am multiplying the nucleon number (protons and neutrons) by 1.67×10271.67 \times 10^{-27} yet this isn't correct.
What am I doing wrong here?

I don't understand where you got those constants from,where did1.67×10^27 come from
(edited 10 months ago)

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