In: Physics
Please show Each Formula and Each Step used to obtain the answer(s).
A hydrogen atom consists of a single proton and a single electron separated on the average by 0.578 x 10-10 meters. Calculate the acceleration of the electron due to the force. Write answer(s) to two decimal places and in the form of (1.6E-19) if applicable/where needed.
let the distance between electron and proton is d
then , d = 0.578 x 10-10 m.
now we know that charges on electron and proton are same only their sign is opposite
charge on proton is positive and charge on electron is negative.
and the magnitude of charge on electron and proton is = 1.6 x 10-16 Coulombs.
so let charge on both is Q.
=> Q = 1.6 x 10-16 Coulombs.
from electrostatic we know :
electrostatic force (F) = (1 * Q * Q) / (4 * * * d2 )
=> F = [ 1 * (1.6 x 10-16) * (1.6 x 10-16) ] / [ 4 * 3.14 * (8.85 x 10-12) * (0.578 x 10-10)2]
=> F = (2.56 x 10-32) / (3.71 x 10-31)
=> F = 0.069 N
now this electrostatic force make the electron to move :
so let the accelration of electron is = a , and mass = m which is equal to 9.1 x 10-31 kg.
so from newtons second law of motion we know :
F = m * a
=> a = F / m
=> a = 0.069 / (9.1 x 10 -31)
=> a = 7.58 x 1028 m/s.