Question

The mass of a proton is 1.00728 atomic mass units (amu) and the mass of a neutron is 1.00867 amu. what is the mass defect (in amu) of a 60/27 Co nucleus (60 is mass #, 27 is atomic #) whose nuclear mass is 59.9338 amu? What is the mass defect in kilograms? What is the energy equivalent of this mass in kilojoules?

Honestly, I have no clue how to work this problem...

Answer 1

Is there a certain formula I can use to solve this?

Answer 2

When protons, neutrons and electrons combine, the atom they form has less mass than the sum of the mass of the protons, neutrons and electrons. The difference is mass defect and is lost as energy.
Given the atomic number (the number of protons) and mass number of Co, you can work out how many neutrons there are.

Answer 3

There are 33 neutrons

Answer 4

So what's the sum of the mass of 33 neutrons and 27 protons?

Answer 5

60.48247 (I multiplied each by their atomic mass which came to 33.28611 + 27.19656)

Answer 6

*I mean 60.48267

Answer 7

So the mass difference is 60.4827 - 59.9338 [u], right?

Answer 8

You just have to convert it to kg and kJ. 1u = 1.6605*10^(-27) kg

Answer 9

Is that really all? It seems like there should be more to it. Aren't the number of electrons supposed to be included in that?

Answer 10

Yeah, I forgot about electrons. Sorry. The mass of an electron is 0.000548579909 u.

Answer 11

So I multiply that by 27, too? Unfortunately, that number is too big too enter into my calculator :/

Answer 12

I know there are the same number of protons as there are electrons... and then I add them together. After I find out how to calculate that number, I just need to know how to convert it to kilograms...

Answer 13

Alright, that's a much simpler number ;P

Answer 14

So now my number is 60.49617

Answer 15

I added 0.0135 to my original number

Answer 16

ahem...i don't think the electrons are important for the mass defect.

if i am correct, the mass defect is the difference between the mass of an actual nucleus and the sum of the masses of the protons and the neutrons.

in any case, the sum of the electron masses "cancels out". we only have to focus on the nucleus.

Answer 17

Just checked a book. gsoda's right.

Answer 18

Okay, so don't include the 0.0135 in the calculations... got it. I got 1.004338 x 10^-25 kg as my final answer. I multiplied 60.48267 by 1 amu (1.660539 x 10^-27)

Answer 19

For the last part, I just convert that number to kilojoules right? Do you know the formula for that?

Answer 20

I don't know how many kilojoules 1 u is. But 1u = 931.5 MeV/c^2 and 1 eV = 1.60*10^(-19) J.

Answer 21

by definition (i think), 1 amu times avogadro's number equals 1 gram.

so 1 amu = 1 gram / avogadro's number

then convert to kilogram. hope it helps!

Answer 22

thanks liquid helium!

Answer 23

Haha for what? I should be thanking you. And Anonymous1921