318675
A group IV A element with a density of \(11.35 \mathrm{~g} / \mathrm{cm}^{3}\) crystallises in a face-centred cubic lattice whose unit cell edge length is \(4.95^{\circ} \mathrm{A}\). The gram atomic mass of the element is
1 \(280.8 \mathrm{~g} / \mathrm{mol}\)
2 \(207.2 \mathrm{~g} / \mathrm{mol}\)
3 \(180 \mathrm{~g} / \mathrm{mol}\)
4 \(109.9 \mathrm{~g} / \mathrm{mol}\)
Explanation:
\(d=\dfrac{G A M \times Z}{N_{A} \times a^{3}}\) For fcc, \(\mathrm{Z}=4\) \(\mathrm{GAM}=207.2 \mathrm{~g} / \mathrm{mol}\).
CHXII01:THE SOLID STATE
318676
The \({\mathrm{\gamma}}\)-form of iron has fcc structure (edge length 386 pm ) and \({\mathrm{\beta}}\)-form has bcc structure (edge length 290 pm ). The ratio of density in \({\mathrm{\gamma}}\)-form and \({\mathrm{\beta}}\)-form is ____ .
1 0.525
2 0.725
3 1.25
4 0.9788
Explanation:
\({\mathrm{Z_{\text {eff }}}}\) for \({\mathrm{\mathrm{fcc}=4}}\) and for bcc \({\mathrm{=2 /}}\) unit cell \(\frac{{{\rho _\gamma }}}{{{\rho _\beta }}}{\rm{ = }}\frac{{{\rho _{{\rm{fcc}}}}}}{{{\rho _{{\rm{bcc}}}}}}{\rm{ = }}\frac{{{{\rm{Z}}_{{\rm{eff }}({\rm{fcc}})}}}}{{{{\rm{Z}}_{{\rm{eff }}({\rm{bcc}})}}}} \times {\left( {\frac{{{{\rm{a}}_{{\rm{bcc}}}}}}{{{{\rm{a}}_{{\rm{fcc}}}}}}} \right)^{\rm{3}}}\) \( = \frac{4}{2} \times {\left( {\frac{{290}}{{386}}} \right)^3} = 0.9788\)
CHXII01:THE SOLID STATE
318677
A metal crystallises in face centred cubic structure with metallic radius \(\sqrt {\rm{2}} \mathop {\rm{A}}\limits^{\rm{^\circ }} \). The volume of the unit cell (in \(\mathrm{m}^{3}\) ) is
1 \(6.4 \times 10^{-29}\)
2 \(4 \times 10^{-29}\)
3 \(6.4 \times 10^{-30}\)
4 \(4 \times 10^{-10}\)
Explanation:
For \(f c c\) unit cell, edge length is \[ \begin{aligned} & a=2 \sqrt{2} r \\ & \mathrm{a}=2 \sqrt{2} \times \sqrt{2} \Rightarrow 4 \stackrel{\circ}{\mathrm{A}} \Rightarrow 4 \times 10^{-10} \mathrm{~m} \end{aligned} \] Volume of unit cell \(=a^{3}\) \[ \begin{aligned} & =\left(4 \times 10^{-10}\right)^{3}=64 \times 10^{-30} \mathrm{~m}^{3} \\ & =6.4 \times 10^{-29} \mathrm{~m}^{3} \end{aligned} \]
KCET - 2020
CHXII01:THE SOLID STATE
318678
A metal crystallises into two cubic phases, face-centered cubic (FCC) and body-centred cubic (BCC) whose unit cell lengths are 3.5 and 3.0 Å respectively. The ratio of the densities of FCC and \(\mathrm{BCC}\) is
1 2.0
2 1.5
3 1.75
4 1.26
Explanation:
\(\dfrac{\rho_{F C C}}{\rho_{B C C}}=\dfrac{Z_{F C C}}{\left(a^{3}\right)_{F C C}} \times \dfrac{\left(a^{3}\right)_{B C C}}{Z_{B C C}}\) \[ =\dfrac{4 \times(3.0)^{3}}{2 \times(3.5)^{3}}=1.26 \]
318675
A group IV A element with a density of \(11.35 \mathrm{~g} / \mathrm{cm}^{3}\) crystallises in a face-centred cubic lattice whose unit cell edge length is \(4.95^{\circ} \mathrm{A}\). The gram atomic mass of the element is
1 \(280.8 \mathrm{~g} / \mathrm{mol}\)
2 \(207.2 \mathrm{~g} / \mathrm{mol}\)
3 \(180 \mathrm{~g} / \mathrm{mol}\)
4 \(109.9 \mathrm{~g} / \mathrm{mol}\)
Explanation:
\(d=\dfrac{G A M \times Z}{N_{A} \times a^{3}}\) For fcc, \(\mathrm{Z}=4\) \(\mathrm{GAM}=207.2 \mathrm{~g} / \mathrm{mol}\).
CHXII01:THE SOLID STATE
318676
The \({\mathrm{\gamma}}\)-form of iron has fcc structure (edge length 386 pm ) and \({\mathrm{\beta}}\)-form has bcc structure (edge length 290 pm ). The ratio of density in \({\mathrm{\gamma}}\)-form and \({\mathrm{\beta}}\)-form is ____ .
1 0.525
2 0.725
3 1.25
4 0.9788
Explanation:
\({\mathrm{Z_{\text {eff }}}}\) for \({\mathrm{\mathrm{fcc}=4}}\) and for bcc \({\mathrm{=2 /}}\) unit cell \(\frac{{{\rho _\gamma }}}{{{\rho _\beta }}}{\rm{ = }}\frac{{{\rho _{{\rm{fcc}}}}}}{{{\rho _{{\rm{bcc}}}}}}{\rm{ = }}\frac{{{{\rm{Z}}_{{\rm{eff }}({\rm{fcc}})}}}}{{{{\rm{Z}}_{{\rm{eff }}({\rm{bcc}})}}}} \times {\left( {\frac{{{{\rm{a}}_{{\rm{bcc}}}}}}{{{{\rm{a}}_{{\rm{fcc}}}}}}} \right)^{\rm{3}}}\) \( = \frac{4}{2} \times {\left( {\frac{{290}}{{386}}} \right)^3} = 0.9788\)
CHXII01:THE SOLID STATE
318677
A metal crystallises in face centred cubic structure with metallic radius \(\sqrt {\rm{2}} \mathop {\rm{A}}\limits^{\rm{^\circ }} \). The volume of the unit cell (in \(\mathrm{m}^{3}\) ) is
1 \(6.4 \times 10^{-29}\)
2 \(4 \times 10^{-29}\)
3 \(6.4 \times 10^{-30}\)
4 \(4 \times 10^{-10}\)
Explanation:
For \(f c c\) unit cell, edge length is \[ \begin{aligned} & a=2 \sqrt{2} r \\ & \mathrm{a}=2 \sqrt{2} \times \sqrt{2} \Rightarrow 4 \stackrel{\circ}{\mathrm{A}} \Rightarrow 4 \times 10^{-10} \mathrm{~m} \end{aligned} \] Volume of unit cell \(=a^{3}\) \[ \begin{aligned} & =\left(4 \times 10^{-10}\right)^{3}=64 \times 10^{-30} \mathrm{~m}^{3} \\ & =6.4 \times 10^{-29} \mathrm{~m}^{3} \end{aligned} \]
KCET - 2020
CHXII01:THE SOLID STATE
318678
A metal crystallises into two cubic phases, face-centered cubic (FCC) and body-centred cubic (BCC) whose unit cell lengths are 3.5 and 3.0 Å respectively. The ratio of the densities of FCC and \(\mathrm{BCC}\) is
1 2.0
2 1.5
3 1.75
4 1.26
Explanation:
\(\dfrac{\rho_{F C C}}{\rho_{B C C}}=\dfrac{Z_{F C C}}{\left(a^{3}\right)_{F C C}} \times \dfrac{\left(a^{3}\right)_{B C C}}{Z_{B C C}}\) \[ =\dfrac{4 \times(3.0)^{3}}{2 \times(3.5)^{3}}=1.26 \]
318675
A group IV A element with a density of \(11.35 \mathrm{~g} / \mathrm{cm}^{3}\) crystallises in a face-centred cubic lattice whose unit cell edge length is \(4.95^{\circ} \mathrm{A}\). The gram atomic mass of the element is
1 \(280.8 \mathrm{~g} / \mathrm{mol}\)
2 \(207.2 \mathrm{~g} / \mathrm{mol}\)
3 \(180 \mathrm{~g} / \mathrm{mol}\)
4 \(109.9 \mathrm{~g} / \mathrm{mol}\)
Explanation:
\(d=\dfrac{G A M \times Z}{N_{A} \times a^{3}}\) For fcc, \(\mathrm{Z}=4\) \(\mathrm{GAM}=207.2 \mathrm{~g} / \mathrm{mol}\).
CHXII01:THE SOLID STATE
318676
The \({\mathrm{\gamma}}\)-form of iron has fcc structure (edge length 386 pm ) and \({\mathrm{\beta}}\)-form has bcc structure (edge length 290 pm ). The ratio of density in \({\mathrm{\gamma}}\)-form and \({\mathrm{\beta}}\)-form is ____ .
1 0.525
2 0.725
3 1.25
4 0.9788
Explanation:
\({\mathrm{Z_{\text {eff }}}}\) for \({\mathrm{\mathrm{fcc}=4}}\) and for bcc \({\mathrm{=2 /}}\) unit cell \(\frac{{{\rho _\gamma }}}{{{\rho _\beta }}}{\rm{ = }}\frac{{{\rho _{{\rm{fcc}}}}}}{{{\rho _{{\rm{bcc}}}}}}{\rm{ = }}\frac{{{{\rm{Z}}_{{\rm{eff }}({\rm{fcc}})}}}}{{{{\rm{Z}}_{{\rm{eff }}({\rm{bcc}})}}}} \times {\left( {\frac{{{{\rm{a}}_{{\rm{bcc}}}}}}{{{{\rm{a}}_{{\rm{fcc}}}}}}} \right)^{\rm{3}}}\) \( = \frac{4}{2} \times {\left( {\frac{{290}}{{386}}} \right)^3} = 0.9788\)
CHXII01:THE SOLID STATE
318677
A metal crystallises in face centred cubic structure with metallic radius \(\sqrt {\rm{2}} \mathop {\rm{A}}\limits^{\rm{^\circ }} \). The volume of the unit cell (in \(\mathrm{m}^{3}\) ) is
1 \(6.4 \times 10^{-29}\)
2 \(4 \times 10^{-29}\)
3 \(6.4 \times 10^{-30}\)
4 \(4 \times 10^{-10}\)
Explanation:
For \(f c c\) unit cell, edge length is \[ \begin{aligned} & a=2 \sqrt{2} r \\ & \mathrm{a}=2 \sqrt{2} \times \sqrt{2} \Rightarrow 4 \stackrel{\circ}{\mathrm{A}} \Rightarrow 4 \times 10^{-10} \mathrm{~m} \end{aligned} \] Volume of unit cell \(=a^{3}\) \[ \begin{aligned} & =\left(4 \times 10^{-10}\right)^{3}=64 \times 10^{-30} \mathrm{~m}^{3} \\ & =6.4 \times 10^{-29} \mathrm{~m}^{3} \end{aligned} \]
KCET - 2020
CHXII01:THE SOLID STATE
318678
A metal crystallises into two cubic phases, face-centered cubic (FCC) and body-centred cubic (BCC) whose unit cell lengths are 3.5 and 3.0 Å respectively. The ratio of the densities of FCC and \(\mathrm{BCC}\) is
1 2.0
2 1.5
3 1.75
4 1.26
Explanation:
\(\dfrac{\rho_{F C C}}{\rho_{B C C}}=\dfrac{Z_{F C C}}{\left(a^{3}\right)_{F C C}} \times \dfrac{\left(a^{3}\right)_{B C C}}{Z_{B C C}}\) \[ =\dfrac{4 \times(3.0)^{3}}{2 \times(3.5)^{3}}=1.26 \]
318675
A group IV A element with a density of \(11.35 \mathrm{~g} / \mathrm{cm}^{3}\) crystallises in a face-centred cubic lattice whose unit cell edge length is \(4.95^{\circ} \mathrm{A}\). The gram atomic mass of the element is
1 \(280.8 \mathrm{~g} / \mathrm{mol}\)
2 \(207.2 \mathrm{~g} / \mathrm{mol}\)
3 \(180 \mathrm{~g} / \mathrm{mol}\)
4 \(109.9 \mathrm{~g} / \mathrm{mol}\)
Explanation:
\(d=\dfrac{G A M \times Z}{N_{A} \times a^{3}}\) For fcc, \(\mathrm{Z}=4\) \(\mathrm{GAM}=207.2 \mathrm{~g} / \mathrm{mol}\).
CHXII01:THE SOLID STATE
318676
The \({\mathrm{\gamma}}\)-form of iron has fcc structure (edge length 386 pm ) and \({\mathrm{\beta}}\)-form has bcc structure (edge length 290 pm ). The ratio of density in \({\mathrm{\gamma}}\)-form and \({\mathrm{\beta}}\)-form is ____ .
1 0.525
2 0.725
3 1.25
4 0.9788
Explanation:
\({\mathrm{Z_{\text {eff }}}}\) for \({\mathrm{\mathrm{fcc}=4}}\) and for bcc \({\mathrm{=2 /}}\) unit cell \(\frac{{{\rho _\gamma }}}{{{\rho _\beta }}}{\rm{ = }}\frac{{{\rho _{{\rm{fcc}}}}}}{{{\rho _{{\rm{bcc}}}}}}{\rm{ = }}\frac{{{{\rm{Z}}_{{\rm{eff }}({\rm{fcc}})}}}}{{{{\rm{Z}}_{{\rm{eff }}({\rm{bcc}})}}}} \times {\left( {\frac{{{{\rm{a}}_{{\rm{bcc}}}}}}{{{{\rm{a}}_{{\rm{fcc}}}}}}} \right)^{\rm{3}}}\) \( = \frac{4}{2} \times {\left( {\frac{{290}}{{386}}} \right)^3} = 0.9788\)
CHXII01:THE SOLID STATE
318677
A metal crystallises in face centred cubic structure with metallic radius \(\sqrt {\rm{2}} \mathop {\rm{A}}\limits^{\rm{^\circ }} \). The volume of the unit cell (in \(\mathrm{m}^{3}\) ) is
1 \(6.4 \times 10^{-29}\)
2 \(4 \times 10^{-29}\)
3 \(6.4 \times 10^{-30}\)
4 \(4 \times 10^{-10}\)
Explanation:
For \(f c c\) unit cell, edge length is \[ \begin{aligned} & a=2 \sqrt{2} r \\ & \mathrm{a}=2 \sqrt{2} \times \sqrt{2} \Rightarrow 4 \stackrel{\circ}{\mathrm{A}} \Rightarrow 4 \times 10^{-10} \mathrm{~m} \end{aligned} \] Volume of unit cell \(=a^{3}\) \[ \begin{aligned} & =\left(4 \times 10^{-10}\right)^{3}=64 \times 10^{-30} \mathrm{~m}^{3} \\ & =6.4 \times 10^{-29} \mathrm{~m}^{3} \end{aligned} \]
KCET - 2020
CHXII01:THE SOLID STATE
318678
A metal crystallises into two cubic phases, face-centered cubic (FCC) and body-centred cubic (BCC) whose unit cell lengths are 3.5 and 3.0 Å respectively. The ratio of the densities of FCC and \(\mathrm{BCC}\) is
1 2.0
2 1.5
3 1.75
4 1.26
Explanation:
\(\dfrac{\rho_{F C C}}{\rho_{B C C}}=\dfrac{Z_{F C C}}{\left(a^{3}\right)_{F C C}} \times \dfrac{\left(a^{3}\right)_{B C C}}{Z_{B C C}}\) \[ =\dfrac{4 \times(3.0)^{3}}{2 \times(3.5)^{3}}=1.26 \]
