How much meat Samuel eats?

Its a straightforward question, right? True. We need to keep a tab on Samuel’s dietary intake, count the calories, as simple as that.

What if Samuel lived in 5000 BC, I am not kidding, except perhaps we need to be sure on the name. Its no more a straightforward question nevertheless answerable.

It uses a few steps, which are nonetheless viable given our tremendous and amazing scientific strides. Go home, and make a list, we will perform this task of finding the dietary habits of primitive men and women.

1. Collect bone samples of primitive inhabitants.
2. Arrange a mass-spectrometer
3. Be ready to be amazed, the spectrometer allows to distinguish between elemental mass of samples based on the property of magnetic objects.

Science fact 1; The bone contains two types of nitrogen called isotopes of nitrogen based on their elemental mass composition. One is Nitrogen-15 slightly heavier than the Nitrogen-14. A specified number of Nitrogen-14 would differ by only 1 gm for every 14 gm, if we replace them by same number of nitrogen-15. By eating meat one goes on accumulating the heavier Nitrogen. In other words for every specified number of these elements the guy would accumulate 1 more gram of nitrogen, if he were to eat meat. SO by eating meat one is only replacing more and more nitrogen-14 by the heavier nitrogen-15

Science fact 2; The magnetic force acts only on charges. And only when the charges are in relative motion to the magnetic source. If a magnet repels the conductor that carries an electric current its only because the charges in the current conductor are in motion wrt the magnet. The magnet does not like that, it tries to disturb the charges. If one tries to move the current conductor in a sense opposite to in which the charges are moving, the magnet would no more repel (or attract) the conductor. Magnet is happy the charges are not squabbling and disturbing its sleep.

But magnets have a limitation in how they impact the running and squabbling charges. The magnetic force is merely a  direction changer. It never changes the speed of the charges in motion. Remember all forces have one or both of the mandate, change speed of an object, change direction of an object, it just changes the velocity of any object, in short force changes the state of inertia, and state of inertia is simply the velocity vector. Nothing more nothing less, mass is just the ability of any object to retain its state of inertia against a given force, But inertia is velocity, the speed plus direction of an object in motion.

Its a really strong force, magnetic force, compared eg to gravity, it exerts as much as 1000 billions times more acceleration than acceleration due to gravity.

That means it can twist the direction of anything that much more times, for a given gravity force equaling to the given magnetic force. Its the only reason why magnetic forces are called far more stronger than the weakest known fundamental force, Gravity.

Remember that it is acceleration which directly gives how much the path of any object can be twisted (that is, made into circles or part circles). The maximum twist occurs when the acceleration or force is directed perpendicular to any objects motion. This is because Force and acceleration have same direction. But when it comes to tasting a force’s strength one must find its acceleration, not just the force, because for same amount of force, a heavier mass would suffer less twist or deflection from its original path.

For same amount of gravity force and magnetic force, for same mass, gravity hardly clenches the desire of the mass to go in any possible circle, but magnetic force does it billions of times stronger.

But for differing amount of mass, the magnetic force on these masses are same, magnetic force would depend only on their charge, only when these are running and squabbling, but its the magnetic acceleration (or the ability to twist the path of the running charges) which is bigger on smaller mass and smaller on bigger mass.

As a result smaller mass suffering from larger magnetic twisting of their paths would end up in smaller circles (smaller circle means bigger twisting, you have to twist stronger to make something in a smaller circle) but bigger mass would suffer lesser twisting or lesser curvature or lesser acceleration from the magnet and end up in bigger circle.

So bigger mass bigger circle, smaller mass smaller circle. You can easily rotate a thin guy in a circle, but to rotate a bigger guy in the same circle would mean a force of bigger magnitude. (magnitude can pertain to same force in different situations, but strength pertains to different forces, if different strength are talked about)

So things seem to be in their perspective as we imagine them to be in our day to day world. Remember Magnetic forces origin in the quantum, where its counter intuitive. But their classical effect match our expectations. Nice world.

Its this property of an extremely strong force (for the same magnitude of gravity and magnetic force, gravity is billions times weaker) that magnetic force is, and the classical property of twisting less if mass is bigger, which is useful in studying the meat eating habits of ancient people.

The Nitrogen-15 which is 1 gm heavier (per Avogadro number of the isotope, called a mole) than the Nitrogen-14, the lighter isotope, gets accumulated more due to eating meat.

The mass spectrometer employs the above principle of magnetic behavior.

The electric sources have a complimentary behavior as compared to the ones of magnetic force. This time the electric forces whose mandate is to change the inertia (remember inertia means velocity, not mass, mass is the ability to preserve the inertia) of the objects in motion, can change the inertia by changing either inertia of speed (called inertia of motion) or inertia of direction.

But we would employ the electric force to change the inertia of direction, to bring back the direction of the charge to what it was, when  magnet deflects the path of the charge.

So by having a suitable arrangement of the electric and magnetic sources, one makes sure all charges can come with same velocity. This arrangement is called a velocity selector and used in the spectrometer. It acts on the principle that when electric and magnetic regions are suitably oriented, the only velocity that gets selected is the ratio of the values of the electric and magnetic strengths, called as fields.

The arrangement allows any charge as long as the charge is not neutral. Thus the mass and charge of the running charges do not decide what the velocity of the charges will be in a velocity selector, and whether or not they will be allowed. As long as they come in with the specified speed v (which is equal to the ratio of the electric strength and magnetic strength E/B ) they continue unabated from the deflection of the magnetic field and at the only allowed speed v = E/B.

When the N-15 (meat component) and N-14 (non meat component) now reach the end of the E/B arrangement called a velocity selector, they await their wonderland destiny. They meet another magnetic merry go round. This time the value of strength of the magnetic region is different. But whatever it is, it takes the N-14 and N-15 on different paths. As we discussed a heavier mass goes through smaller deflection, hence bigger circle.

N-14 and N-15 accumulate at different points, on the spectrometer so that we know how much meat the primitive fella ate.

I did a little calculation to show exactly how the spectrometer justifies this reasoning. It creates a 2 cm difference in where accumulation of the isotopes occur, for a said 1 gm difference in their molar weights. 