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:

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

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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

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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

Electricity and Magnetism

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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.