Question

Assume that the nucleus of the flourine atom is a sphere of radius $5\times {10}^{-13}cm$. What is the density of matter in the nucleus?

• A. $6.02\times {10}^{23}g/mL$
• B. $6.02\times {10}^{13}g/mL$
• C. $12.02\times {10}^{23}g/mL$
• D. $12.02\times {10}^{13}g/mL$

Answer 1

Answer: (B)

$6.02\times {10}^{13}g/mL$

Density= mass/volume

Mass of $1$ mole $F$ nuclei = $19g/mol$

$1Fatom$

=$\frac{19g/mol}{6.022\times {10}^{23}atoms/mol}$

$=\frac{19g/atom}{6.022\times {10}^{23}}=3.155\times {10}^{-23}g/atom$

Volume of sphere of $F$ nucleus = $\frac{4}{3}\times 3.14\times (5\times {10}^{-13}{)}^3$

$=\frac{4}{3}\times 3.14\times 125\times {10}^{-39}c{m}^3$

$=5.23\times {10}^{-37}c{m}^3$

$=5.23\times {10}^{-37}ml$ $[\because 1c{m}^3=1ml]$

Density = $\frac{3.155\times {10}^{-23}g}{5.23\times {10}^{-37}ml}=0.603\times {10}^{14}$

$=6.03\times {10}^{13}g/ml$

$\therefore$ Answer is option B.