To determine the radii of a univalent ion- Pauling gave a method as follows-i- In an ionic crystal of the type M - X - cations and anions are in contact with each other- Therefore- the sum of their ionic radius is equal to the interionic distance-ii- r M - r X - C - Z eff M - C - Z eff X - pm Z eff is the effective nuclear charge Z eff - Z - - where - is the screening constant- For Ne - -4-5- r M - C - Z eff M - and r X - C - Zeff X -The actual interionic distance in MgO should be-A- 256 pmB- Lesser than 256 pmC- 372 pmD- 276 pm

The correct option is B Lesser than 256 pmc=6.5×4.5×230/11pm r_M^++r_X^ =d_MgO=c[1/(12 4.5)+1/(8 4.5)] d_MgO=[6.5×4.5×230/11×11/(7.5×3.5)]=256 pm nbsp; Sinc ...

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Standard XII

Chemistry

Cationic Radius

To determine ...

Question

To determine the radii of a univalent ion, Pauling gave a method as follows:
i. In an ionic crystal of the type $M^{+} X^{-}$ , cations and anions are in contact with each other. Therefore, the sum of their ionic radius is equal to the interionic distance.
ii. $r_{M}^{+} + r_{X}^{-} = \frac{c}{Z_{e f f} (M^{+})} + \frac{c}{Z_{e f f} (X^{-})}$ pm $Z_{e f f}$ is the effective nuclear charge $Z_{e f f} = Z - σ$ ; where $σ$ is the screening constant. For $Ne, σ = 4.5$
$∴ r_{M}^{+} = \frac{c}{Z_{eff} (M^{+})}$ and $r_{X}^{-} = \frac{c}{Z e f f (X^{-})}$

The actual interionic distance in $M g O$ should be:

256 pm

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276 pm

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Lesser than 256 pm

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372 pm

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Solution

The correct option is C Lesser than 256 pm
$c = \frac{6.5 \times 4.5 \times 230}{11} p m$
$r_{M}^{+} + r_{X}^{-} = d_{M g O} = c [\frac{1}{(12 - 4.5)} + \frac{1}{(8 - 4.5)}]$
$d_{M g O} = [\frac{6.5 \times 4.5 \times 230}{11} \times \frac{11}{(7.5 \times 3.5)}] = 256 p m$
Since $M g^{2 +}$ and $O^{2 -}$ are bivalent ions, force of attraction between them are greater than the monovalent ions.
Actual $d_{M g O} < 256 p m$

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Similar questions

Q. To determine the radii of a univalent ion, Pauling gave a method as follows:
i. In an ionic crystal of the type

M^{+} X^{-}

, cations and anions are in contact with each other. Therefore, the sum of their ionic radius is equal to the interionic distance.
ii.

r_{M}^{+} + r_{X}^{-} = \frac{c}{Z_{e f f} (M^{+})} + \frac{c}{Z_{e f f} (X^{-})}

Z_{e f f}

is the effective nuclear charge

Z_{e f f} = Z - σ

; where

σ

is the screening constant. For

Ne, σ = 4.5

∴ r_{M}^{+} = \frac{c}{Z_{eff} (M^{+})}

and

r_{X}^{-} = \frac{c}{Z e f f (X^{-})}

The actual interionic distance in

M g O

should be:

Q. As per Pauling, the radius of an isoelectronic ion in a given crystal is inversely proportional to the effective nuclear charge,

Z^{*}

Z^{*} = Z - σ

; where

σ

represents the screening constant. The crystal structure of

NaF

is shown as below :

The radius of

F^{-}

in pm is

(130 + x)

. The value of

x

in nearest possible integer is

Q. The formula for an effective nuclear charge is:

(if

σ

is screening constant)

Q. Which is true about effective nuclear charge.
(A)

Z_{e f f} = Z - σ

(is Screening Constant)
(B)

Z_{e f f}

increases as we move from left to right in Periodic Table
(C)

Z_{e f f}

decreases from top to bottom
(D)

Z_{e f f}

increases from top to bottom

Q. The ionic radius of

C l^{-}

ion is

1.81 A^{0}

. The interionic distance of

N a C l

and

N a F

are

2.79 A^{0}

and

2.31 A^{0}

respectively. The ionic radius of

F^{-}

ion will be:

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The correct option is C Lesser than 256 pmc=6.5×4.5×23011pm r+M+r−X=dMgO=c[1(12−4.5)+1(8−4.5)] dMgO=[6.5×4.5×23011×11(7.5×3.5)]=256 pm Since Mg2+ and O2− are bivalent ions, force of attraction between them are greater than the monovalent ions. Actual dMgO<256 pm