Tuesday, August 2, 2011

Mustard Seeds

This is a simple packet of mustard seeds. Do you notice that some of the seeds are clinging the side of the packet? Simply open and pour a packet of Mustard seeds and then you will see this happening.
Why are these seeds hanging around!? What stops them from falling to the bottom like the rest of the seeds? What gives them repulsive force to oppose the force of gravity?
It doesn't happen like this, for example, for a salt or a sugar packet.
In case of mustard seeds, what is happening is, the seeds are getting charged up, and the charge stays on them for a while, after which they become neutral. The charging is due to stripping off of an electron or two from the lattice of the mustard seed.
Can you estimate how much is the force generated because of charges separated in the case of mustard seeds shown in packet?
Assume that two seeds are 1 cm apart, and 1 seed's force on the other is balancing its weight.
m= mass = density * volume = 0.426902 gm/cm^3 * volume from this link.
g= 980 cm/s^2
k= 1 in case of CGS units
q= charge to be found out
Rad= radius or mustard seed = 1 mm say = 0.1 cm

hence q^2= density*volume*g* r^2

hence q= sqrt(0.426902 * (4/3)*3.14 * 10^(-3) * 980 * 1^2)
= 1.132346 statCoulomb

and using 1 StatCoulomb = 0.1 Am/c ≈ 3.3364×1010 C
and charge on one electron , e = 1.6 * 10 ^ (-19) C, we get

q = 1.132346 * 3.3364 * (10 ^ 10 ) C = 3.77796e+10 C which is a huge charge! so the mustard seeds are not hanging on the sides because of repulsive forces. They are sharing particular positions on the plastic cover. What must be happening is that the electrons are stripped off the mustard seed, and deposited on the plastic cover. The same equation with r = 1 0 Angstrom (Typical lattice planes separation distances are in this range, e.g. from this ref.) then becomes

r= 10 Angstrom = 10 * 10^(-10) m = 10 * 10 ^ (-8) cm = 10^(-7) cm

q = sqrt ( 0.426902 * (4/3)*3.14 * 10^(-3) * 980 * 10^(-14) )
= 1.32 * 10 ^(-7) stat coulomb

= 1.32 * 10 ^(-7)* 3.3364 * (10 ^ 10 ) C

= 4415 C= 3806 * 10^19 e
which is also huge.

So what must be happening is, even at smaller level, say 1 Angstrom , the electrons are stripped off and deposited to the plastic cover. Then some kind of temporary chemical bondings must be happening, since we approach molecular distances at that level.

Notice how in this simple physical situation in front, we could calculate and figure out what's happening in there. Thus physics helps you to be a Sherlock Holmes in the nature's mysterious ways of functioning!