Chapter 15: Q13MP (page 777)

A radioactive source emits $1800 α$ particles during an observation lasting 10 hours. In how many one-minute intervals do you expectno $α' s$ ? $5 α' s$ ?

Short Answer

Expert verified

The values required is given below.

$\begin{matrix} N_{0} = 30 \\ N_{5} = 60 \end{matrix}$

Step by step solution

Given Information

A radioactive source emits $1800 α$ particles during an observation lasting 10 hours.

Definition of the Poisson distribution.

A discrete frequency distribution that indicates the likelihood of a set of independent occurrences occurring at a specific moment.

Find the values.

The formula for Poisson distribution states that. $P_{n} = \frac{μ^{n} e^{- μ}}{n!}$

The average is given below.

$\begin{array}{l} μ = \frac{1800}{10 \times 60} \\ μ = 3 \end{array}$

Probabilities are given below.

$\begin{matrix} P_{0} = e^{- 3} \\ = 0.0498 \\ P_{5} = \frac{{(3)}^{5} e^{- 3}}{5!} \\ = 0.1 \end{matrix}$

The number of the interval is given below.

$\begin{matrix} N_{0} = (0.0498) (10) (60) \\ = 30 \\ N_{5} = (0.1) (10) (60) \\ = 60 \end{matrix}$

The values required is given below.

$\begin{matrix} N_{0} = 30 \\ N_{5} = 60 \end{matrix}$

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A radioactive source emits $1800 α$ particles during an observation lasting 10 hours. In how many one-minute intervals do you expectno $α' s$ ? $5 α' s$ ?

Short Answer

Step by step solution

Given Information

Definition of the Poisson distribution.

Find the values.

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A radioactive source emits 1800αparticles during an observation lasting 10 hours. In how many one-minute intervals do you expectnoα's? 5α's?

Short Answer

Step by step solution

Given Information

Definition of the Poisson distribution.

Find the values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Physics of Motion

Physical Quantities And Units

Electrostatics

Atoms and Radioactivity

Particle Model of Matter

Study anywhere. Anytime. Across all devices.

A radioactive source emits $1800 α$ particles during an observation lasting 10 hours. In how many one-minute intervals do you expectno $α' s$ ? $5 α' s$ ?