Calcium has a face centered cubic (cubic close-packed) structure and a density o
ID: 526219 • Letter: C
Question
Calcium has a face centered cubic (cubic close-packed) structure and a density of 1.54 g/cm^3. What is the atomic radius of calcium? A. 384 pm B. 197 pm C. 333 pm D. 296 pm E. 99 pm A sample of wood from an old Egyptian tomb is found to have a carbon- 14 activity of 7.07 disintegrations per minute per gram of C, while a sample of wood from a newly cut tree has a carbon-14 activity of 15.3 disintegrations per minute per gram of C. The halt-life of carbon-14 is 5730 years. Calculate the age of the old wood. A. 5100 years B. 6400 years C. 3600 years D. 7200 years E. 9200 years Calculate the pH of a 2.50 M aqueous solution of the salt methyammonium chloride, CH_3NH_3Cl. K_b for methylamine, CH_3NH_2, is 4.2 times 10^-4. A. 1.60 B. 3.38 C. 5.11 D. 7.00 E. 10.62Explanation / Answer
17)
density,
d = (Z*M)/(a^3*NA)
where d is density in g/cm^3
Z is 1 for cubic lattice, 2 for bcc and 4 for fcc
a is edge length in cm
M is molar mass in g/mol = 40.1 g/mol
NA is Avogadro’s constant
USE:
d = (Z*M)/(a^3*NA)
1.54= (4*40.1)/(a^3 * 6.022*10^23)
a^3 = 1.7296*10^-22
a = 5.572*10^-8 cm
a = 557.2 pm
for fcc:
length of face diagonal = 4*r
sqrt(a^2+a^2) = 4*r
sqrt (557.2^2 + 557.2^2) = 4*r
4*r = 787.9
r = 197 pm
Answer: B
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