Nuclear physics - number of nucleons on surface?

[aliaze1]

Homework Statement

For a nucleus of A=220, estimate very roughly how many nucleaons would be at the surface.

Homework Equations

R₀=1.5 x 10^-15

r=A^1/3 x R₀

The Attempt at a Solution

Using the formulas, I calculated R to be 7.2441729 x 10^-15

The book says that the number of nucleons at the surface and the total number of nucleons has a ratio of ~1/r

1/r= 1.3804 x 10¹⁴

I tried the following:

1.3804 x 10¹⁴ = 220/x

which didn't make sense...

what am I doing wrong?

Thanks!

 

[Dick]

I think the key here is 'very roughly'. You have a big sphere made of 220 smaller spheres. Roughly, what's the volume of that sphere in terms of the radius of the smaller sphere. What's the total area of that sphere? Each smaller sphere exposes, roughly, pi*r^2 of outer surface area. How many are there? Roughly.

 

[aliaze1]

so I could set a volume of a sphere as 220, solve for r, and then find the surface area based on that?

 

[Dick]

so I could set a volume of a sphere as 220, solve for r, and then find the surface area based on that?

Yes, then use the area to estimate the number of spheres with volume 1 on the surface. I think that's what they're after. It's certainly a 'rough estimate'.

 

[aliaze1]

thanks!