Question:easy

A pebble has an average diameter of 8 mm. Its \(\phi\)-value on the Udden-Wentworth scale is ___________ (answer in integer).

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Use \(\phi = -\log_2(d)\), with the diameter d in millimetres.
Updated On: Jul 20, 2026
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Correct Answer: -3

Solution and Explanation

Step 1: Remember what phi means in plain terms.
On the Udden-Wentworth scale, phi is the power of $2$ that gives the grain size in millimetres, with a negative sign placed in front. In other words, if $d = 2^{n}$ mm, then $\phi = -n$.

Step 2: Write 8 as a power of 2.
The pebble is $8$ mm across, and
\[ 8 = 2 \times 2 \times 2 = 2^{3} \]
so $n = 3$.

Step 3: Apply the sign rule.
Since $\phi = -n$, we get
\[ \phi = -3 \]

Step 4: Sanity check against the scale.
On this scale, granules and pebbles, that is grains bigger than $2$ mm, always carry negative phi values, and $-3$ sits right in that coarse range, so the number makes sense.
\[ \boxed{\phi = -3} \]
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