Consider that an electron is revolving in an excited state of Hydrogen atom with velocity 25.6 10^5 ms ⁻¹ . The radius of the orbit is x 10⁻⁹ m. The value of x is : [Take the mass of electron to be 9 10⁻³¹ kg, charge of electron =-1.6 10⁻¹⁹ C and 1 4 ₀ =9 10^9 N m ^2 C ⁻² ]

Step-by-step solution

The electrostatic force between the nucleus and the electron provides the necessary centripetal force for the electron to revolve in its orbit. mv^2 r = 1 4 ₀ e^2 r^2 Rearranging for the radius r : r = 1 4 ₀ e^2 mv^2 Substituting the given values: 1 4 ₀ = 9 10^9 N m ^2 C ⁻² e = 1.6 10⁻¹⁹ C m = 9 10⁻³¹ kg v = 25.6 10^5 m s ⁻¹ r = 9 10^9 (1.6 10⁻¹⁹)^2 9 10⁻³¹ ( 25.6 10^5)^2 r = 9 10^9 2.56 10⁻³⁸ 9 10⁻³¹ 25.6 10¹⁰ r = 2.56 10⁻²⁹ 25.6 10⁻²¹ r = 0.1 10⁻⁸ m r = 1 10⁻⁹ m Comparing this with r = x 10⁻⁹ m, we get: x = 1 Ans