What is the radius of the nuclide ?

Question

What is the radius of the nuclide  ?

Quizplus · Accepted Answer

The given nuclide notation represents a nucleus with 11 protons and a mass number of 32 (which would mean 21 neutrons). Knowing this, we can use the empirical formula for nuclear radius:

r = r0*A^(1/3)

where r0 is a constant (approximately 1.2 fm) and A is the mass number of the nucleus. Plug in the values we have:

r = 1.2*32^(1/3)
r = 1.2*3.174
r = 3.81 fm

However, we have to adjust for the fact that protons repel each other due to their positive charges, so the actual radius will be slightly larger than this. Taking into account the number of protons, we can use the following correction factor:

rcorrected = r*(1 + 0.75*(Z^(2/3))/A^(1/3))

where Z is the number of protons and A is the mass number. Plug in the values we have:

rcorrected = 3.81*(1 + 0.75*(11^(2/3))/32^(1/3))
rcorrected = 5.4 fm

So the correct answer is B.

What Is the Radius of the Nuclide