# Find the unknown isotope.

• einsteinoid
In summary, the conversation discusses finding the nucleus with a radius that is one half that of a given isotope of dysprosium, with atomic number 66 and atomic mass 159.952202 u. The formula for the radius of a nucleus in terms of its atomic number is given, and the steps to find the unknown nucleus are outlined. A mistake in using the atomic number instead of the atomic mass is identified and corrected, resulting in the correct answer being identified as option A: Ne (A=20, Z=10).

## 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!

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

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

Ahhhhhh, of course. Thanks again rl.bhat!

## 1. What is an isotope?

An isotope is a variation of an element that has the same number of protons but a different number of neutrons. This results in a different atomic mass for the isotope.

## 2. How do you find the unknown isotope?

To find the unknown isotope, you can use various scientific techniques such as mass spectrometry or nuclear magnetic resonance (NMR) spectroscopy. These methods can determine the mass and composition of the isotope.

## 3. Why is it important to find the unknown isotope?

Finding the unknown isotope can provide valuable information about the composition and behavior of an element. It can also help scientists understand the stability and reactivity of isotopes, which can have practical applications in fields such as medicine and energy production.

## 4. Can isotopes be artificially created?

Yes, isotopes can be artificially created through processes such as nuclear reactions or particle bombardment. This allows scientists to create isotopes that do not naturally occur and study their properties.

## 5. What are some common uses of isotopes?

Isotopes have a wide range of uses in fields such as medicine, industry, and research. Some common uses include radioactive isotopes in medical imaging, stable isotopes in tracing chemical reactions, and radioactive isotopes in power generation.