Chapter 42: Q 4 Exercise (page 1236)

Calculate the mass, radius, and density of the nucleus of $(a) {}^{7}{Li} and (b)^{207} Pb$ .
Give all answers in SI units.

Short Answer

Expert verified

Hence, the mass, radius and density is:

$a.) m = 9.988 \times 10^{- 27} kg, r = 2.18 \times 10^{- 15} m, ρ = 2.3 \times 10^{17} kg / m^{3} b.) m = 3.437 \times 10^{- 25} kg, r = 7.1 \times 10^{- 15} m, ρ = 2.3 \times 10^{17} kg / m^{3}$

Step by step solution

Given information

$(a) {}^{7}{Li} and (b)^{207} Pb$

$m ({}^{6}{Li}) = 6.0135 u m ({}^{207}{Pb}) = 206.9309 u r_{o} = 1.2 fm \to 1.2 \times 10^{- 15} m$

Explanation

a.) We have to find value of $m, r and ρ for {}^{6}{Li} :$

The mass is:

m = 6.0135 u (\frac{1.661 \times 10^{- 27} kg}{1 u}) m = 9.988 \times 10^{- 27} kg

The radius is:

r = r_{o} A^{1 / 3} r = (1.2 \times 10^{- 15} m) (6)^{1 / 3} r = 2.18 \times 10^{- 15} m

The density is

$ρ = \frac{m}{\frac{4}{3} π r^{3}} ρ = \frac{9.988 \times 10^{- 27} kg}{\frac{4}{3} π {(2.18 \times 10^{- 15} m)}^{3}} ρ = 2.3 \times 10^{17} kg / m^{3}$

Explanation

b.) We have to find value of $m, r and ρ for {}^{207}{Pb} :$

The mass is:

$m = 206.9309 u (\frac{1.661 \times 10^{- 27} kg}{1 u}) m = 3.437 \times 10^{- 25} kg$

The radius is:

$r = r_{o} A^{1 / 3} r = (1.2 \times 10^{- 15} m) (207)^{1 / 3} r = 7.1 \times 10^{- 15} m$

The density is:

$ρ = \frac{m}{\frac{4}{3} π r^{3}} ρ = \frac{3.437 \times 10^{- 25} kg}{\frac{4}{3} π {(7.1 \times 10^{- 15} m)}^{3}} ρ = 2.3 \times 10^{17} kg / m^{3}$

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.

Calculate the mass, radius, and density of the nucleus of $(a) {}^{7}{Li} and (b)^{207} Pb$ .
Give all answers in SI units.

Short Answer

Step by step solution

Given information

Explanation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Measurements

Nuclear Physics

Electricity

Circular Motion and Gravitation

Radiation

Study anywhere. Anytime. Across all devices.

Calculate the mass, radius, and density of the nucleus of (a)Li7and(b)207Pb.Give all answers in SI units.

Short Answer

Step by step solution

Given information

Explanation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Measurements

Nuclear Physics

Electricity

Circular Motion and Gravitation

Radiation

Study anywhere. Anytime. Across all devices.

Calculate the mass, radius, and density of the nucleus of $(a) {}^{7}{Li} and (b)^{207} Pb$ .
Give all answers in SI units.