What is the Binding Energy of an Oxygen Atom Given its Mass Defect?

[brake4country]

Homework Statement

The difference between the mass of one oxygen atom and the sum of the masses of its parts is approx. 2.27 x 10^-28 kg. What is the binding energy that holds an oxygen atom together? (The charge on one electron is 1.6x10^-19 C).

Homework Equations

E = mc^2

The Attempt at a Solution

I started off with listing my knowns:
mass = 2.27 x 10^-28 kg
E = what we're solving for
c = 3 x 10^8 m/s

E = (2.27 x 10^-28)(3.8 x 10^8)^2
18.54 x 10^-14 = 1.85 x 10^-15 J

To convert Joules to eV, I divide by the charge on one electron:
(1.85 x 10^-15)/(1.6 x 10^-19) = 1.2 x 10^4 eV.

My book says it's 1.2 x 10^8 eV but I don't know why.

 

[SteamKing]

Homework Statement

The difference between the mass of one oxygen atom and the sum of the masses of its parts is approx. 2.27 x 10^-28 kg. What is the binding energy that holds an oxygen atom together? (The charge on one electron is 1.6x10^-19 C).

Homework Equations

E = mc^2

The Attempt at a Solution

I started off with listing my knowns:
mass = 2.27 x 10^-28 kg
E = what we're solving for
c = 3 x 10^8 m/s

E = (2.27 x 10^-28)(3.8 x 10^8)^2
18.54 x 10^-14 = 1.85 x 10^-15 J

To convert Joules to eV, I divide by the charge on one electron:
(1.85 x 10^-15)/(1.6 x 10^-19) = 1.2 x 10^4 eV.

My book says it's 1.2 x 10^8 eV but I don't know why.

Your formulas are correct, but you need to double check your arithmetic.

In your calculation of E, you have written c = 3.8×10⁸ m/s, instead of 3×10⁸ m/s

My calculation of E gets a different number of joules. I think once you have calculated the correct value for E, your problems will disappear.

 

[collinsmark]

I think you have the right idea, except something seems to be going awry with your arithmetic.

Homework Statement

The difference between the mass of one oxygen atom and the sum of the masses of its parts is approx. 2.27 x 10^-28 kg. What is the binding energy that holds an oxygen atom together? (The charge on one electron is 1.6x10^-19 C).

Homework Equations

E = mc^2

The Attempt at a Solution

I started off with listing my knowns:
mass = 2.27 x 10^-28 kg
E = what we're solving for
c = 3 x 10^8 m/s

E = (2.27 x 10^-28)(3.8 x 10^8)^2

wait, where did the 3.8 × 10⁸ figure come from?

18.54 x 10^-14 = 1.85 x 10^-15 J

That answer seems to be different whether you used 3.8 × 10⁸ or 3.0 × 10⁸.

So you should check your calculations again on that one.

To convert Joules to eV, I divide by the charge on one electron:
(1.85 x 10^-15)/(1.6 x 10^-19) = 1.2 x 10^4 eV.

My book says it's 1.2 x 10^8 eV but I don't know why.

I got 1.2 × 10⁸ eV, ignoring a little rounding difference.

[Edit: SteamKing beat me to the response. ]

 

[brake4country]

Ah yes, the error with ^-28 and ^16. That was just careless but thank you both for finding that! I got 1.2 x 10^8 as my final answer. (Also, 3.8 x 10^8 was a typo).