A given metal crystallizes out with a cubic structure having edge length of $361$ pm. If there are four metal atoms in one unit cell, what is the radius of one atom?

80

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108

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40

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127.6

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Solution

The correct option is C $127.6$ pm
Since there are four metal atoms in one unit cell, the unit cell is fcc type.

For fcc unit cell, radius $r = 0.3535 a$ , where $a$ is the edge length of the unit cell.

Hence, $r = 0.3535 \times 361$ pm $= 127.6$ pm

Thus, the radius of one atom is $127.6$ pm.

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A given metal crystallizes out with a cubic structure having edge length of 361 pm. If there are four metal atoms in one unit cell, what is the radius of one atom?

The correct option is C 127.6 pmSince there are four metal atoms in one unit cell, the unit cell is fcc type.For fcc unit cell, radius r=0.3535 a, where a is the edge length of the unit cell.Hence, r=0.3535×361 pm =127.6 pmThus, the radius of one atom is 127.6 pm.

A given metal crystallizes out with a cubic structure having edge length of $361$ pm. If there are four metal atoms in one unit cell, what is the radius of one atom?

The correct option is C $127.6$ pm
Since there are four metal atoms in one unit cell, the unit cell is fcc type.

For fcc unit cell, radius $r = 0.3535 a$ , where $a$ is the edge length of the unit cell.

Hence, $r = 0.3535 \times 361$ pm $= 127.6$ pm

Thus, the radius of one atom is $127.6$ pm.