Homer’s Hair Arrggh! Where’s my hair gone?

Ohhh! Why won’t it grow faster?

What is this hair stuff anyway?

Homer’s Hair Structure

The main component of hair is keratin. Keratins are proteins made of long chains (polymers) of amino acids. They account for approximately 85% of Homer’s hair with the remainder comprising water, fats, vitamins and trace elements.

Homer’s hair seen under an electron microscope.

Homer’s hair structure.

Homer’s Amino acidsAmino what?

Where are they?

Will they hurt me?

Homer’s Amino AcidsAmino-acids are small biomolecules. There are 16 different amino acids found in keratin.

Amino

group

Carboxyl

group

‘R’ group

Hydrogen

Homer’s Amino AcidsSo, how many do I need?

Can I eat them?

Mmmmmm amino acids.

How many amino acids does it take for 1 hair to grow for 1 second?

Let’s do the CalculationWhat shape is your hair Homer?

Cubic Cylindrical

OK we agree it is a cylinder. So we can work out a volume of hair grown per month using

пr2h

For this we need to know the length of hair grown per month and the radius of a hair

Choose a length (mm) 1 10 100

Choose a radius (mm) 1 0.05 0.0001

Volume of Hair per month

You grow about 10 mm of hair per month and the radius of one hair is about 0.05 mm (it takes about the width of 10 hairs is about 1 mm.

Therefore the Volume of hair grown per month is

= П x (0.05)2 x 10

= 0.0785 mm3

Mass of HairWe now need to transform this volume into a mass. What relates mass and volume?

Refractive index Density Body Fat Index

So we need to know the density of hair – does it float or sink in water? Well it does a bit of both (surface tension is a problem) which suggests the density of hair is about the same as water which is 1 g/cm3 – careful of the units Homer, convert it into g/mm3

1 g/cm3 = 0.001 g/mm3

So the mass of hair grown per month is

Mass = density x volume

= 0.001 g/mm3 x 0.0785 mm3

= 0.000 0785 g

Mass per second OK so we know how much mass each hair puts on per month, but we need to know how much mass per second.

How many seconds in a month Homer?

About 30 days, 24 hrs per day, 60 minutes per hour, 60 seconds per minute

30 x 24 x 60 x 60 = 2592000 seconds per month

Therefore

Mass of hair per sec = 0.000 0758 / 2592000

= 0.000 000 000 0302 g

Moles

As you know Homer hair is made of keratin which is a protein made up of amino acids. To work out the number of moles of amino acids per second we need to know the relative molecular mass (RMM) of amino acids. As this is a rough calculation we will use the average RMM of 135 g/mole.

So now we have a mass of hair per second we need to work out the number of molecules.

To work out the number of molecules we first need to work out the number of moles.

number of moles = mass of hair / RMM

Moles to Molecules

Number of moles of amino acids

= 0. 000 000 000 0302 g 135 g/mole

= 0.000 000 000 000 224 moles

OK Homer are you ready for this.

Not much Hey? Now to convert it into molecules

Moles to Molecules

= 0.000 000 000 000 224 x 603 000 000 000 000 000 000 000

Avogadro was the first to work out how many molecules were in a mole. He found that in one mole there are

603 000 000 000 000 000 000 000

Molecules

We now call this Avogadro’s Number

The Answer = 135 000 000 000

amino acids per second

That’s

135 Billion

Homer’s donut towerWhich is a very large number Homer!

If each amino acid was a donut! Arrrrgggghhhh!Then you could make a donut tower 4,375,000 km tall. Enough to reach the moon 11

times!

Ok amino acids

do your thing!