Chapter 5: Q. 5.90 (page 166)

The radioscope sodium- $24$ is used to determine the levels of electrolytes in the body. $A 16$ - $μ g$ sample of sodium- $24$ decays to $2.0 μ g$ in $45 h$ . What is the half-life, in hours, of sodium- $24$ ? $(5.4)$

Short Answer

Expert verified

The sodium half-life- $24$ in hours is $t y_{2} ≅ 15 h$

Step by step solution

Step 1:Introduction

Sodium- $24$ radioactive decay A radioactive sodium- $24$ (24 Na) nucleus decay scheme. It decays by beta decay to an excited magnesium-24 (24 Mg) nucleus with a half-life of $15$ hours. Two gamma rays are rapidly emitted, and the excitation energy is carried away, resulting in the stable ground state of magnesium-24 .

Step 2:Given data

Given data is the radioscope sodium- $24$ is used to determine the levels of electrolytes in the body

To find half life sodium- $24$

Step 3:Explanation

Sodium $- 24$ decay follows first orders kinetics

$k = \frac{2.303}{t} \log \frac{N_{0}}{N}$

$t y_{2} = \frac{0.693}{K}$

where $t y_{2} =$ Half life of N $N_{C} - 24$

where $t =$ time elapsed

$N_{0} =$ Initial amount

$N_{s} =$ Amount after time t

$k =$ Rate constant

$\frac{0.693}{t y_{2}} = \frac{2.303}{45 h} \times \log (\frac{164 g}{24 g})$

$t y_{2} ≅ 15 h$

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The radioscope sodium- $24$ is used to determine the levels of electrolytes in the body. $A 16$ - $μ g$ sample of sodium- $24$ decays to $2.0 μ g$ in $45 h$ . What is the half-life, in hours, of sodium- $24$ ? $(5.4)$

Short Answer

Step by step solution

Step 1:Introduction

Step 2:Given data

Step 3:Explanation

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The radioscope sodium-24is used to determine the levels of electrolytes in the body.A16- μgsample of sodium-24decays to2.0μgin 45h. What is the half-life, in hours, of sodium-24? (5.4)

Short Answer

Step by step solution

Step 1:Introduction

Step 2:Given data

Step 3:Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Chemistry Branches

Chemical Analysis

Inorganic Chemistry

The Earths Atmosphere

Organic Chemistry

Kinetics

Study anywhere. Anytime. Across all devices.

The radioscope sodium- $24$ is used to determine the levels of electrolytes in the body. $A 16$ - $μ g$ sample of sodium- $24$ decays to $2.0 μ g$ in $45 h$ . What is the half-life, in hours, of sodium- $24$ ? $(5.4)$