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Chapter 29: Problem 9

Find the radius and volume of the \(_{43}^{107}\) Te nucleus.

Short Answer

Expert verified
Question: Calculate the radius and volume of the nucleus of a Tellurium-107 atom. Answer: The radius of the Tellurium-107 nucleus is approximately \(5.66 \times 10^{-15}\) meters, and the volume of the nucleus is approximately \(9.59 \times 10^{-43}\) cubic meters.

Step by step solution

01

Identify given values and the formula.

We have the given nucleus \(_{43}^{107}\) Te with mass number \(A = 107\). We will use the nuclear radius formula: $$ R = R_0 A^{1/3} $$ Step 2: Plug in the values and find the radius.
02

Input values into the formula.

Now, we will plug in the values: \(A = 107\) and \(R_0 = 1.2 \times 10^{-15}\,\text{m}\). We will then solve for \(R\): $$ R = (1.2\times 10^{-15}\,\text{m}) (107)^{1/3} $$ Step 3: Calculate the radius.
03

Solve for the radius.

On solving the above expression, we obtain: $$ R \approx 5.66 \times 10^{-15}\,\text{m} $$ Step 4: Calculate the volume of the nucleus.
04

Use the radius to find the volume.

We have found the radius of the nucleus, so we can now use it to find the volume of the nucleus using the formula: $$ V = \frac{4}{3}\pi R^3 $$ Step 5: Plug in the radius value and find the volume
05

Input values into the volume formula.

Now, substituting the value of \(R\) into the formula: $$ V = \frac{4}{3}\pi (5.66 \times 10^{-15}\,\text{m})^3 $$ Step 6: Calculate the volume.
06

Solve for the volume.

On solving the above expression, we obtain: $$ V \approx 9.59 \times 10^{-43}\,\text{m}^3 $$ So, the radius of the \(_{43}^{107}\) Te nucleus is approximately \(5.66 \times 10^{-15}\) meters, and the volume of the nucleus is approximately \(9.59 \times 10^{-43}\) cubic meters.

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