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 ]
A. 1
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 10^ 10 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 Answer: 1
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