Question

derive an expression for the energy of the electron in a stable orbit in an atom. hence, show that the energy is inversely proportional to (1) the radius of the orbit (2)the square of the principal quantum numbers​

Answer 1

Let an electron revolves with a constant speed v around the nucleus in a stationary orbit of radius r. The electrostatic force acting on the electron is balanced

Answer 2

The energy expression for the electron in a stable orbit in an atom is given as follows-

$E=\dfrac{-2π^2Z^2e^4m}{n^2h^2}$.

• Here Z is the charge of the atom.
• m is the mass of the atom.
• h is called Plank's constant.
• n is called the principal quantum number.
• e is the charge of the electron.
• Thus from the above relationship, it is proved that energy is inversely proportional to the square of the principal quantum number.
• Again the expression of radius for the electron in a stable orbit in an atom is given as follows-
• $r=\dfrac{n^2h^2}{4π^2Ze^2m}$.
• Thus comparing the two expressions of energy and radius can be proved that energy is inversely proportional to the radius of the orbit.
• #SPJ3