Chapter 42: Q 22 Exercise (page 1236)

What is the half-life in days of a radioactive sample with 5.0 x 10¹⁵
atoms and an activity of 5.0 x 10⁸ Bq?

Short Answer

Expert verified

Therefore the half life in days is $80.2 days$

Step by step solution

Given information

$N = 5.0 \times 10^{15} atoms R = 5.0 \times 10^{8} Bq$

Explanation

The activity of a radioactive sample is calculated using

$R = r \cdot N \to (Equation 1.)$

The decay rate is:

$r = \frac{1}{τ} r = \frac{\ln (2)}{t_{1 / 2}} r = \frac{0.693}{t_{1 / 2}} (E q u a t i o n 2 .)$

Calculation

Substituting the equation (2) in equation (1), we get

$R = r \cdot N R = \frac{0.693}{t_{1 / 2}} \cdot N t_{1 / 2} \cdot R = (0.693) \cdot N t_{1 / 2} = \frac{(0.693) \cdot N}{R} t_{1 / 2} = \frac{(0.693) \cdot (5.0 \times 10^{15} atoms)}{(5.0 \times 10^{8} Bq)} t_{1 / 2} = 6.93 \times 10^{6} s t_{1 / 2} = 6.93 \times 10^{6} s \times \frac{1 day}{86400 s} t_{1 / 2} = 80.2 days$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

What is the half-life in days of a radioactive sample with 5.0 x 10¹⁵
atoms and an activity of 5.0 x 10⁸ Bq?

Short Answer

Step by step solution

Given information

Explanation

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Fluids

Rotational Dynamics

Work Energy and Power

Particle Model of Matter

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

What is the half-life in days of a radioactive sample with 5.0 x 1015atoms and an activity of 5.0 x 108 Bq?

Short Answer

Step by step solution

Given information

Explanation

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Fluids

Rotational Dynamics

Work Energy and Power

Particle Model of Matter

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

What is the half-life in days of a radioactive sample with 5.0 x 10¹⁵
atoms and an activity of 5.0 x 10⁸ Bq?