How can neutron be converted to proton and electron? Since a neutron and a proton are made up of quarks and an electron is a lepton, how can a neutron yield an electron?
 A: A neutron is made of 3 quarks, two up quarks and one down.  The process you are talking about is called beta decay.  It is a weak nuclear interaction the can be summarized like this:
$$(u+d+u) \rightarrow (u+d+d) + e^- + \bar{\nu}$$
One of the up quarks ($u$) decays producing a down quark ($d$), an electron ($e^-$), and an anti-neutrino ($\bar\nu$).  The final baryon state has has two down quarks and one up, that's a proton.  This process follows a few conservation laws.


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*conservation of baryon number: $1 \rightarrow 1$, Each quark counts for $1/3$ of a baryon number.  The three-quark proton and neutron are each $1$ baryon. This maintains the same number of quarks on each side of the arrow.

*conservation of lepton number $0 \rightarrow +1 -1$. A neutrino is also a lepton, and an anti-particle counts as $-1$ of it's type.  So the electron and anti-neutrino add up to zero total leptons on the right-hand-side.

*conservation of charge $0 \rightarrow +1 -1 +0$. The $(udu)$ neutron and the anti-neutrino have zero charge.  The $(udd)$ proton has $+1$ charge and the electron has $-1$, so the charge is zero on both sides of the arrow.

*conservation of energy $E_n \rightarrow E_p + E_e + E_\nu$. The total energy of the particles on each side is the same.


Energy conservation is a bit more that just that.  All of the particles have mass, so they have energy following following $E=mc^2$.  Additionally, they could have kinetic energy if they are moving.
If the initial neutron is at rest, then its energy is $E_n=(1.008664\,\mathrm{u})c^2 = 939.6$ MeV, where $\mathrm{u}$ is the atomic mass unit and MeV is a mega-electron-volt, a unit of energy.
A proton at rest has an energy of $E_p = 938.3$ MeV, and an electron at rest has $E_e = 0.5$ MeV.  Nobody knows the rest mass of a neutrino, but it's at least a million times less than an electron.  We'll call it zero, even though it's not...
When we put this together assuming everything is at rest, we get:
$$ 939.6\,\mathrm{MeV} \rightarrow 938.3\,\mathrm{MeV} + 0.5\,\mathrm{MeV} + 0\,\mathrm{MeV} $$
But wait, the two sides aren't equal.  The right-hand-side is missing $0.8$ MeV.  To conserve energy the new particles must be moving, so they have a little bit of kinetic energy to make up the mass-Energy difference.
A: A nuclear decay is not something that already exists being pulled out of a particle. It is the creation of new particles. As long as the transition respects all of the conservation laws there is a probability of it happening. 
