Question

I am looking for the number of neutrons of a second isotope. The specific charge = total charge of nucleus/mass of nucleus = 3.7x10^7

total charge of nucleus = 92 x 1.6x10^-19
mass of nucleus = A x 1.67x10^-27 where,
A = number of neutrons + number of protons

You need to rearrange and find A, then subtract the number of protons, the answer should be about 146 neutrons. Can anyone help?

Answer 1

the charge of the nucleus is entirely due to the number of protons

The charge in coulombs is \(92 \times 1.6\times10^{-19} C\)

\(1.6\times10^{-19} C\) is the magnitude of the charge of an electron or a proton

divide the total charge of the nucleus by the charge of the proton to find the number of protons in the nucleus

\[Z=\frac{92 \times 1.6\times10^{-19} C}{1.6\times10^{-19} C} \]

Answer 2

\[A=Z+N\]

Answer 3

That equals 92?

Answer 4

yes 92 protons, so that can only correspond to one element right, can you find the element on a periodic table,?

Answer 5

Yes that is uranium?

Answer 6

that is right \(^A_{92}U\).

the mass of the nucleus in kilograms
\(m=A \times 1.67\times10^{-27} kg\)

the atomic mass unit \[u=1.67\times 10^{-27} kg\]

Answer 7

Ok whats next?

Answer 8

you should get \(m=Au\)
simply dived by \(u\) to get \(A\)

Answer 9

and set the two equations for \(A\) equal to one another ,
all that is left is to solve for the number of neutrons \(N\)

Answer 10

Yes i know. The number of neutrons is 146. I already have the answer. 146=92=238! BUT to get 146 you have to come to the calculation of 238 how do i solve that?

Answer 11

total charge of nucleus/mass of nucleus \(=Ze/m\)

Answer 12

Ok. That is 92 *e/m?

Answer 13

\[\frac{Ze}{m}=\frac{Ze}{Au}=\frac ZA\frac eu=3.7\times10^7 (C/kg)\]

Answer 14

Yes that,s correct 3.7*10^7 (C/kg). What next?

Answer 15

solve for \(a\) remember \(a\) should be 238

Answer 16

Yes i know. How do we solve A?

Answer 17

i ment capital \(A\) not \(a\)

Answer 18

Ok A

Answer 19

\[A=\frac {Ze}{3.7\times10^{7}u} \]

Answer 20

Yes that = 3.97*10-25 is that correct?

Answer 21

im getting confused

Answer 22

Ok. 92*1.6*10^7/3.7*10^7 =3.97*10^-25. Or am i doing something wrong here?

Answer 23

no that is good , my mistake
\[A=\frac{Ze}{qu}=\frac{92\times1.6\times10^{-19}}{3.7\times10^7u}=\frac{3.97\times10^{-25}}{u} \rightarrow \frac{3.97\times10^{-25}}{1.67×10^{−27}kg}=\dots \]

Answer 24

i kinda messed up the units a bit though

Answer 25

=237.72 or 238. Yes!Yes!Yes thank god someone gets it at last. Well done

Answer 26

\[A=\frac{Z\cdot e[C]}{q[C/kg]\cdot u[kg]}=\frac{92~\cdot~1.6\times10^{-19}[C]}{3.7\times10^{7}~\cdot~ 1.67\times10^{-27}[1/C]}=238\]

Answer 27

Well done. You deserve more than one medal for persevering with it!

Answer 28

And we have our answer \[^{238}_{92}U\]
unfortunatly not as useful as \(^{235}_{92}U\)
but at least it will last longer

Answer 29

Yes. Till the next time