Chapter 42: Q 28 Exercise (page 1236)

An unstable nucleus undergoes alpha decay with the release
of 5.52 MeV of energy. The combined mass of the parent and
daughter nuclei is 452 u. What was the parent nucleus?

Short Answer

Expert verified

Therefore, the parent $nucleus with mass of 228 u is {}^{228}{Th} .$

Step by step solution

Given information

$K_{α} = 5.52 MeV m ({}^{4}H_{e}) = 4.002602 u m_{X} + m_{Y} = 452 u$

Explanation

We use the formula:

$K_{α} = Δ m c^{2} K_{α} = (m_{X} - m_{Y} - m H_{e}) c^{2} 5.52 MeV = (m_{X} - m_{Y} - m H_{e}) 5.52 \frac{MeV}{c^{2}} (\frac{1 u}{931.5 \frac{MeV}{c^{2}}}) = (m_{X} - m_{Y} - m H_{e}) 0.0059259 u = (m_{X} - m_{Y} - m H_{e}) m_{X} - m_{Y} = 0.0059259 u + m ({}^{4}H_{e}) m_{X} - m_{Y} = 0.0059259 u + 4.002602 u m_{X} - m_{Y} = 4.0085279 u$

We got a system of two equations:

$m_{X} + m_{Y} = 452 u m_{X} - m_{Y} = 4.0085279 u$

Calculations

We will find the value of m_X:

$2 m_{X} = 452 u + 4.0085279 u 2 m_{X} = 456.008529 u m_{X} = \frac{456.008529 u}{2} \Rightarrow m_{X} = 228.0042645 u$

$So, nucleus with mass of 228 u is {}^{228}{Th} .$

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An unstable nucleus undergoes alpha decay with the release
of 5.52 MeV of energy. The combined mass of the parent and
daughter nuclei is 452 u. What was the parent nucleus?

Short Answer

Step by step solution

Given information

Explanation

Calculations

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An unstable nucleus undergoes alpha decay with the releaseof 5.52 MeV of energy. The combined mass of the parent anddaughter nuclei is 452 u. What was the parent nucleus?

Short Answer

Step by step solution

Given information

Explanation

Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Scientific Method Physics

Wave Optics

Circular Motion and Gravitation

Electric Charge Field and Potential

Modern Physics

Study anywhere. Anytime. Across all devices.

An unstable nucleus undergoes alpha decay with the release
of 5.52 MeV of energy. The combined mass of the parent and
daughter nuclei is 452 u. What was the parent nucleus?