A uranium-238 nucleus undergoes a radioactive decay, 238 U 234Th + 4He. The masses are approximately 238, 234 and 4 u, where u = the atomic mass unit. The U nucleus is initially at rest. Suppose the He nucleus has speed v. Then what is the kinetic energy of the Th nucleus? Parameters: u = 1.66 x 10-27 kg; v = 9.000×106 m/s. (in J)

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A uranium-238 nucleus undergoes a radioactive decay, \(^{238}\text{U} \longrightarrow \,^{234}\text{Th} + \,^{4}\text{He}\).

The masses are approximately 238, 234, and 4 u, where u = the atomic mass unit.

The U nucleus is initially at rest. Suppose the He nucleus has speed v. Then what is the kinetic energy of the Th nucleus?

**Parameters:**

\[ 
\text{[Expression obscured] } 
\]

\[ 
u = 1.66 \times 10^{-27} \, \text{kg}; \, v = 9.000 \times 10^6 \, \text{m/s}.
\]

(in J)

**Options:**

- A: \(2.942 \times 10^{-15}\)
- B: \(3.678 \times 10^{-15}\)
- C: \(4.597 \times 10^{-15}\)
- D: \(5.746 \times 10^{-15}\)
- E: \(7.183 \times 10^{-15}\)
- F: \(8.978 \times 10^{-15}\)
- G: \(1.122 \times 10^{-14}\)
- H: \(1.403 \times 10^{-14}\)
Transcribed Image Text:A uranium-238 nucleus undergoes a radioactive decay, \(^{238}\text{U} \longrightarrow \,^{234}\text{Th} + \,^{4}\text{He}\). The masses are approximately 238, 234, and 4 u, where u = the atomic mass unit. The U nucleus is initially at rest. Suppose the He nucleus has speed v. Then what is the kinetic energy of the Th nucleus? **Parameters:** \[ \text{[Expression obscured] } \] \[ u = 1.66 \times 10^{-27} \, \text{kg}; \, v = 9.000 \times 10^6 \, \text{m/s}. \] (in J) **Options:** - A: \(2.942 \times 10^{-15}\) - B: \(3.678 \times 10^{-15}\) - C: \(4.597 \times 10^{-15}\) - D: \(5.746 \times 10^{-15}\) - E: \(7.183 \times 10^{-15}\) - F: \(8.978 \times 10^{-15}\) - G: \(1.122 \times 10^{-14}\) - H: \(1.403 \times 10^{-14}\)
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