Q12.119CP Barium is the largest nonradioac... [FREE SOLUTION]

Chapter 12: Q12.119CP (page 497)

Barium is the largest nonradioactive alkaline earth metal. It has a body-centred cubic unit cell and a density of $3.62 g / {cm}^{3}$ . What is the atomic radius of barium? (Volume of a sphere: $V = \frac{4}{3} {蟺谤}^{3}$ .)

Short Answer

Expert verified

The atomic radius is the distance from the nucleus to the atom and has the value $5 脳 10^{鈭� 8}$ m.

Step by step solution

Definition

Density can be defined as the ratio of mass to volume. It is inversely proportional to the volume of the unit cell as the mass of the atom is constant.

$蚁 = \frac{Z 脳 M}{Na 脳 a^{3}}$

For BCC, the value of $Z=2$ is the number of atoms in contact in a particular structure.

The atomic radius of barium.

Given,

Density of the unit cell, 蚁= ${3.62g/cm}^{3}$

Avogadro number, N_a = $6.02 脳 10^{23}$ atoms/molecules

Molar mass of atom or molecule, m = 137 g/mole

As,

$\begin{matrix} 蚁 = \frac{Z 脳 M}{Na 脳 a^{3}} \\ 3.62 = \frac{2 脳 137}{6.02 脳 10^{23} 脳 a^{3}} \end{matrix}$

Hence,

role="math" localid="1658992140786" $\begin{matrix} a^{3} = \frac{2 脳 137}{6.02 脳 10^{23} 脳 3.62} \\ a = (125 脳 1 0^{- 24})^{\frac{1}{3}} \\ a = 5 脳 10^{鈭� 8} \end{matrix}$

The atomic radius of the body-centered unit cell is $5 脳 10^{鈭� 8}$ m.

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91影视

Barium is the largest nonradioactive alkaline earth metal. It has a body-centred cubic unit cell and a density of $3.62 g / {cm}^{3}$ . What is the atomic radius of barium? (Volume of a sphere: $V = \frac{4}{3} {蟺谤}^{3}$ .)

Short Answer

Step by step solution

Definition

The atomic radius of barium.

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91影视

Barium is the largest nonradioactive alkaline earth metal. It has a body-centred cubic unit cell and a density of 3.62g/cm3. What is the atomic radius of barium? (Volume of a sphere: V=43蟺谤3 .)

Short Answer

Step by step solution

Definition

The atomic radius of barium.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Kinetics

Chemical Analysis

Physical Chemistry

Ionic and Molecular Compounds

Organic Chemistry

Chemical Reactions

Study anywhere. Anytime. Across all devices.

Barium is the largest nonradioactive alkaline earth metal. It has a body-centred cubic unit cell and a density of $3.62 g / {cm}^{3}$ . What is the atomic radius of barium? (Volume of a sphere: $V = \frac{4}{3} {蟺谤}^{3}$ .)