IMAT 2018 Q57 [Diameter]

Three spherical particles have the following diameters: 1650 pm, 1.5 nm and 0.0036 µm.

What is their order of diameter (smallest first)?

A. 0.0036 µm, 1.5 nm, 1650 pm
B. 1.5 nm, 0.0036 µm, 1650 pm
C. 1650 pm, 1.5 nm, 0.0036 µm
D. 0.0036 µm, 1650 pm, 1.5 nm
E. 1.5 nm, 1650 pm, 0.0036 µm

In order to solve this, we must know how much pm, nm and µm are.

pm = 10 ^ {-12}m
nm = 10 ^ {-9}m
µm = 10 ^ {-6}m

using that information, we will transform all the diameters in m.

1650 pm = 1650 \cdot 10 ^ {-12}m = 1.65\cdot 10 ^ {3 -12}m = 1.65\cdot 10 ^ {-9}m

1.5 nm = 1.5 \cdot 10 ^ {-9}m

0.0036 µm = 3.6 \cdot 10 ^ {-3-6}m = 3.6 \cdot 10 ^ {-9}m

Seeing this and comparing it, we can conclude that the order of the diameter (smallest first) is:

1.5 nm, 1650 pm,0.0036 µm.

so the correct answer is (E)

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