Sun protection factor (SPF) is a measure of the fraction of sunburn producing UV

Question

Sun protection factor (SPF) is a measure of the fraction of sunburn producing UV rays blocked. For example, "SPF 15" means that 1/15th of the burning radiation will reach the skin, assuming sun screen is applied evenly at a thick dosage of 2 milligrams per square centimeter (2.0 mg/cm2).

a) Calculate the theoretical transmittance of the sunscreen.
b) Caculate the theoretical thickness of the sunscreen required on the skin (in cm and µm) if the sunscreen has a density of 1.0 g/mL.
c) Calculate the molar sborptivity of the sunscreen if the effective sunscreen material has a concentration of 1.0 mol/L.

Explanation / Answer

1) the transmittance will be 100 / 15 = 6.67

2) 2mg / cm2 is applied

We know that Density = MAss / Volume

Volume = Area X thickness

So Density = MAss / Area X Thickness

Thickneess = MAss / Area X Density = 2 X 10^-3 / cm2 X 1g / mL = 2X10^-3 cm or 2 micro meter

3) We know that

Absorbance = molar absorptivity X concentration X length

Absorbance = 2 – log(%T)

%T = 1/15 = 6.67

Absorbamce = 2-log(6.67) = 2-0.823 = 1.175

So 1.1759 = molar absorptitivity X 1 X 2 X 10^-3 X 10^-3

Molar absorptivity = 5.87 X 10^5

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