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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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Most popular questions from this chapter

Show that the spontaneous \(\alpha\) decay of \(^{19} \mathrm{O}\) is not possible.
(a) What is the mass defect of the 'H atom due to the binding energy of the electron (in the ground state)? (b) Should we worry about this mass defect when we calculate the mass of the \(^{1} \mathrm{H}\) nucleus by subtracting the mass of one electron from the mass of the \(^{1} \mathrm{H}\) atom?
Which of these unidentified nuclides are isotopes of each other? $$ { }_{71}^{175}(?) $$ $$ \frac{71}{32}(?) $$ $$ \frac{175}{74}(?) $$ $$ { }_{71}^{167}(?) $$ $$ \frac{71}{30}(?) $$ $$ { }_{74}^{180}(?) $$
Radioactive iodine, \(^{131} \mathrm{I},\) with a half-life of $8.0252 \mathrm{d},$ is used in some forms of medical diagnostics. (a) If the initial activity of a sample is \(64.5 \mathrm{mCi},\) what is the mass of $^{131} \mathrm{I}$ in the sample? (b) What will the activity be 4.5 d later?
Identify the daughter nuclide when \(_{19}^{40} \mathrm{K}\) decays via \(\beta^{-}\) decay.
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