The Total solution for NCERT class 6-12
In a hydrogen atom, the electron and proton are bound ata distance of about 0.53 Å:
(a) Estimate the potential energy of the system in eV,taking the zero of the potential energy at infinite separation of the electronfrom proton.
(b) What is the minimum work required to free theelectron, given that its kinetic energy in the orbit is half the magnitude ofpotential energy obtained in (a)?
(c) What are the answers to (a) and (b) above if thezero of potential energy is taken at 1.06 Å separation?
The distance betweenelectron-proton of a hydrogen atom,
Charge on an electron, q1 =−1.6 ×10−19 C
Charge on a proton, q2 =+1.6 ×10−19 C
(a) Potential at infinity is zero.
where,
∈0 is thepermittivity of free space
14πε0=9×109 Nm2C-2∴ Potential energy=0-9×109×1.6×10-1920.53×10-10=-43.47×10-19 J∵1.6×10-19 J=1 eV∴Potential energy=-43.7×10-19=-43.7×10-191.6×10-19=-27.2 eV
Therefore, the potential energy of the system is −27.2eV.
(b) Kinetic energy is half of the magnitude ofpotential energy.
Total energy = 13.6 − 27.2 = 13.6 eV
Therefore, the minimum work required to free the electronis 13.6 eV.
(c) When zero of potential energy is taken,
∴Potential energy of the system = Potential energyat d1 − Potential energy at d