# Find the unknown isotope.

## Homework Statement

A particular isotope of dysprosium has atomic number 66 and atomic mass 159.952202 u. Identify the nucleus with a radius that is one half that of this isotope.

A. Ne (A=20, Z=10) <<<Correct Answer
B. O (A=16, Z=8)
C. Mn (A=50, Z=25)
D. Ni (A=60, Z=28)

## Homework Equations

The only relevant equation I can think of is the equation of a nucleus's radius in terms of its atomic number:

r = (1.2X10^-15)(A^[1/3])

## The Attempt at a Solution

My attempt has gone as follows:

1. Find the radius of the given dysprosium isotope by plugging it's atomic number into the given formula:

r1 = (1.2X10^-15)(66^[1/3])
r1 = 4.849488E-15 m

2. Now I find the radius of the unknown nucleus:

r2 = (1/2)r1
r2 = 2.424744E-15 m

3. Finally, by plugging the r2 value into the original equation, I should be able to solve for the atomic number of the unknown nucleus:

r2 = 2.424744E-15 m = (1.2X10^-15)(A2^[1/3])

A2 = 8.25

This is obviously not correct, it seems I'm missing a step; possibly one involving the atomic mass, since it is mentioned in the problem. Any help would be appreciated.

Thanks!

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rl.bhat
Homework Helper
r1 = (1.2X10^-15)(66^[1/3])
This is wrong. A is atomic mass, not atomic number.

r1 = (1.2X10^-15)(66^[1/3])
This is wrong. A is atomic mass, not atomic number.
Ahhhhhh, of course. Thanks again rl.bhat!