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Difficulty: HardScientific Notation and Unit Conversions

A student in a materials science lab is analyzing the layers of a multi-junction solar cell. The thicknesses of the four distinct layers are measured using different units, as shown in the table below:

Layer NameThickness
Antireflective layer6.0×104 pm6.0 \times 10^4 \text{ pm}
Perovskite layer1.8×10−4 mm1.8 \times 10^{-4} \text{ mm}
Silicon layer3.5×10−7 m3.5 \times 10^{-7} \text{ m}
Contact layer4.2×102 nm4.2 \times 10^2 \text{ nm}

Based on these measurements, arrange the four solar cell layers by thickness from smallest to largest.

  1. 1Antireflective layer (6.0×104 pm6.0 \times 10^4 \text{ pm})
  2. 2Perovskite layer (1.8×10−4 mm1.8 \times 10^{-4} \text{ mm})
  3. 3Silicon layer (3.5×10−7 m3.5 \times 10^{-7} \text{ m})
  4. 4Contact layer (4.2×102 nm4.2 \times 10^2 \text{ nm})

Answer

The correct order of layers from smallest to largest thickness is: Antireflective layer, Perovskite layer, Silicon layer, and Contact layer.
By converting all measurements to standard meters, we get: Antireflective layer = 0.6×10−7 m0.6 \times 10^{-7} \text{ m}, Perovskite layer = 1.8×10−7 m1.8 \times 10^{-7} \text{ m}, Silicon layer = 3.5×10−7 m3.5 \times 10^{-7} \text{ m}, and Contact layer = 4.2×10−7 m4.2 \times 10^{-7} \text{ m}. Comparing these values yields the correct order from smallest to largest thickness: Antireflective, Perovskite, Silicon, and Contact.

Step-by-Step Solution

1
Convert the thickness of the Antireflective layer to meters.
6.0×104 pm=6.0×104×10−12 m=6.0×10−8 m=0.6×10−7 m6.0 \times 10^4 \text{ pm} = 6.0 \times 10^4 \times 10^{-12} \text{ m} = 6.0 \times 10^{-8} \text{ m} = 0.6 \times 10^{-7} \text{ m}
To compare the thicknesses, all values should be converted to the same standard unit (meters). One picometer (1 pm1 \text{ pm}) is equal to 10−12 m10^{-12} \text{ m}.
2
Convert the thickness of the Perovskite layer to meters.
1.8×10−4 mm=1.8×10−4×10−3 m=1.8×10−7 m1.8 \times 10^{-4} \text{ mm} = 1.8 \times 10^{-4} \times 10^{-3} \text{ m} = 1.8 \times 10^{-7} \text{ m}
Convert millimeters to meters. One millimeter (1 mm1 \text{ mm}) is equal to 10−3 m10^{-3} \text{ m}.
3
Ensure the Silicon layer thickness is expressed in the same exponent scale.
3.5×10−7 m3.5 \times 10^{-7} \text{ m}
This value is already in meters with a 10−710^{-7} exponent, making comparison straightforward.
4
Convert the thickness of the Contact layer to meters.
4.2×102 nm=4.2×102×10−9 m=4.2×10−7 m4.2 \times 10^2 \text{ nm} = 4.2 \times 10^2 \times 10^{-9} \text{ m} = 4.2 \times 10^{-7} \text{ m}
Convert nanometers to meters. One nanometer (1 nm1 \text{ nm}) is equal to 10−9 m10^{-9} \text{ m}.
5
Order the converted values from smallest to largest.
0.6×10−7 m<1.8×10−7 m<3.5×10−7 m<4.2×10−7 m0.6 \times 10^{-7} \text{ m} < 1.8 \times 10^{-7} \text{ m} < 3.5 \times 10^{-7} \text{ m} < 4.2 \times 10^{-7} \text{ m}
Comparing the coefficient values multiplied by 10−7 m10^{-7} \text{ m} allows ordering of the layers.

Key Concept

Expressing and comparing measurements by converting prefix units to a standard baseline unit using scientific notation.
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Topics

Scientific Notation and Unit Conversions

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