Which of the following is a correct expression of average particle size with value of p=1 i.e index related to the size of an individual particle and frequency index (f=2):
Show Hint
To find the average particle size, use the formula:
\[
d_{1f} = \frac{\sum n d^{f+1}}{\sum n d^f}
\]
where \( p \) is the size index and \( f \) is the frequency index.
The problem asks for the correct expression of average particle size with an index value of \( p = 1 \). The index \( p \) is related to the size of an individual particle, and the frequency index is given as \( f = 2 \). This suggests that we need to use the appropriate formula for particle size distribution. The general formula for the size index is:
\[
d_{pq} = \frac{\sum n d^{p+q}}{\sum n d^{p+q-1}}
\]
For \( p = 1 \) and \( q = n \), we substitute these values:
\[
d_{s1} = \frac{\sum n d^2}{\sum n d^3}
\] This matches option (B), making it the correct answer.
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