Question

obtain an expression for the kinetic energy of electron in the Bohr model of hydrogen atom (Z=1 ) . ​

Answer 1

Answer:

2.18x10^(-18) J

Explanation:

F = k.q1.q2/r²

electrostatic force of attraction is equal to the centripetal force,

mv²/r = k.q1.q2/r²

implies that, mv² = k.q1.q2/r (r is cancelled on both sides)

implies that, mv² = k.e.(-e)/r (e is the charge if proton)

implies that, mv² = -ke²/r

since we are just comparing the magnitude of force and not the direction, mv² = ke²/r

K.E = ½mv²

implies that, K.E = ½ke²/r

since for an hydrogen atom in its ground state, r = 5.29x10^(-11) m, e = 1.6022x10^(-19) C and k = 9x10^(9) kg⋅m³⋅A²/s⁴,

K.E = 2.18x10^(-18) J