It is found experimentally that 13 6 eV energy is required to seperatea hydrogen atom into a proton and an - Physics - Atoms

Question

It is found experimentally that 13 6 eV energy is required to
seperatea hydrogen atom into a proton and an electron Compute the
orbital radius and the velocity of the electron in a hydrogen atom

Satyendra Singh · Accepted Answer

It can be experimentally verified that it takes 13 6 eV of energy
to remove the electron from a hydrogen atom when it is in its
ground state (closest to the nucleus) If the electron is somehow
moved to higher shells, then it takes less energy to remove it from
its atom This means that if the electron of hydrogen atom is in its
ground state, it takes at least 13 6eV to detach it from its atom
The electron energy is the sum of its K E and P E We may write: P E
+ K E = -13 6 eV, or - k e2r + ½ Mv2 = -13 6 eV, (1) where
v2 can be found by understanding that the Coulombic force between
the proton and electron of the hydrogen atom provides the necessary
centripetal force for the electron spin around the proton Equating
the expression for these two forces yields: ke2 r2 = Mv2r Solving
for v2 yields: v2 = (ke2) (rM) (2) Substituting (2) in (1) changes
(1) to : - k e2 r + ½ M( ke2rM ) = -13 6 eV (3) - (
½) k e2r = -13 6× ( 1 6 × 10 –19 ) Joules
Substituting for (k) and (e), k = 14πε0 = 9×109e =
1 6 × 10 –19yields the value for r of r = 0 53 ×
10 –10m The diameter of H-atom is therefore 1 06 × 10
–10m or 1 06 ÅAlso,from (2) v2 = (ke2) (rM)M = 9 1
× 10-31 kgsubstituting and solving we have,v = 2 2 ×
106 m/s

It is found experimentally that 13.6 eV energy is required to seperatea hydrogen atom into a proton and an electron. Compute the orbital radius and the velocity of the electron in a hydrogen atom.