1 Nuclear Radius The density of nuclear matter can be estimated by assuming A spherical nucleons of radius ro merge into a spherical nu- cleus of the same total volume. This implies the radius of a nucleus that contains A nucleons is r = ro A¹/³. Experimental measurements suggest that ro = 1.2 x 10-¹5 m. (a) Estimate the radius of a He nucleus. (b) Estimate the radius of a 335 U nucleus. (c) Find a stable isotope with a nuclear radius roughly half that of 325 £325U.

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Chapter1: Units, Trigonometry. And Vectors
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## 1. Nuclear Radius

The density of nuclear matter can be estimated by assuming \(A\) spherical nucleons of radius \(r_0\) merge into a spherical nucleus of the same total volume. This implies the radius of a nucleus that contains \(A\) nucleons is \(r = r_0 A^{1/3}\). Experimental measurements suggest that \(r_0 = 1.2 \times 10^{-15}\) m.

### Problems

1. **Estimate the radius of a \( ^4_2 \text{He} \) nucleus.**

2. **Estimate the radius of a \( ^{235}_{92} \text{U} \) nucleus.**

3. **Find a stable isotope with a nuclear radius roughly half that of \( ^{235}_{92} \text{U} \).**
Transcribed Image Text:## 1. Nuclear Radius The density of nuclear matter can be estimated by assuming \(A\) spherical nucleons of radius \(r_0\) merge into a spherical nucleus of the same total volume. This implies the radius of a nucleus that contains \(A\) nucleons is \(r = r_0 A^{1/3}\). Experimental measurements suggest that \(r_0 = 1.2 \times 10^{-15}\) m. ### Problems 1. **Estimate the radius of a \( ^4_2 \text{He} \) nucleus.** 2. **Estimate the radius of a \( ^{235}_{92} \text{U} \) nucleus.** 3. **Find a stable isotope with a nuclear radius roughly half that of \( ^{235}_{92} \text{U} \).**
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