Question

derivate an equation of total energy of revolving electron in the 3rd orbit for Hydrogen​

Answer 1

Explanation:

Consider the electron revolving in the nth orbit around the hydrogen nucleus. Let m and -e be the mass and the charge of the electron, r the radius of th eorbit and v, the liner speed of the

, the linear speed of the electron. <br> According to Bohr's first postulate, centripetal force acting on the electron = electrostatic force of attraction exerted on the electron by the nucleus <br>

... (1) <br> where

is the permittivity of free space. <br>

Kinetic energy (KE) of the electron

...(2) <br> The electric potential due to the hydrogen nucleus (charge = +e) at a point at a distance r from it is

<br>

Potential energy (PE) of the electron <br> =charge on the electron

electric potential <br>

...(3) <br> Hence, the total energy of the electron in the nth orbit is <br>

<br>

...(4) <br> This shows that the total energy of the electron in the nth orbit of hydrogen atom is inversely proportional to the radius of the orbit as

and e are constants. <br> The radius of the nth orbit of the electron is <br>

...(5) <br> where h is Planck's constant. <br> From Eqs. (4) and (5), the energy of the electron in the nth Bohr orbit is <br>

<br>

...(6) <br> The minus sign in the shows that the electron is bound to the nucleus by the electrostatic force of attraction. <br> As m, e,

and h are constant, we get, <br>

<br> i.e., the energy of the electron in a stationary energy state is discrete and is inversely proportional to the square of the principal quantum number.