Answer to Question #241525 in General Chemistry for Maddy

Question

Oxygen has three naturally occurring isotopes call mom oxygen-16, oxygen-17, and oxygen-18, with respective masses of 2.6560x 10^-21 kg, 2.8228x10^-26 kg, and 2.9888x10^-26 kg. What is the mass of an individual proton and individual neutron?

Answer 1

From the data given, we create simultaneous equations as shown

Let the mass of a proton be x and that of a neutron be y;

Thus;

Since oxygen has 8 protons and a varied number of neutrons per isotope;

8x + 8y = 2.6560x10^-21 for ¹⁶O

8x + 9y = 2.8228 x 10^-26

If we solve the simultaneous equation by subtracting

We get;

y = (2.6560x10^-21) - (2.8228 x 10^-26)

= 2.656 x 10^-21

Solving for x;

8x +8(2.656x10^-21) = 2.6560x10^-21

8x=(2.6560x10^-21) - (2.1248x10^-20)

x = 2.324 x 10^-21

Thus the mass of a proton is 2.324 x 10^-21 kg and that of a neutron is 2.656x10^-21 kg