NOTE: In all calculations below use: ko 9.0 x 109 N.m2/C2 electrostatic constant
ID: 1404372 • Letter: N
Question
NOTE: In all calculations below use: ko 9.0 x 109 N.m2/C2 electrostatic constant 1.6 x 10 19 C elementary charge ge G 6.7 x 10 N.m2/kg gravitational constant me 9.1 x 10-31 kg electron's mass mp 1.7 x 10 27 kg proton's mass 1) Consider a classic model of the hydrogen atom, an electron spins around a proton in a prefect circular orbit of radius r 5.3 x 10 11 m Calculate the period of rotation T (in seconds) of the electron (Hint: the electrostatic force between the negatively charged electron and the positively charged proton according to the Third Newton's Law must be equal to the centrifugal force F met where me is the electron's mass, and v is the electron's speed, such that vT 2TTr describes one full rotation.)Explanation / Answer
here,
radius of the orbit , r = 5.3 *10^-11 m
let the speed of electron in the orbit be v
for circular motion
electrostatic force = centrifugal force
me * v^2/r = k * e^2/ r^2
9.1*10^-31 *v^2/( 5.3 *10^-11) = 9 * 10^9 * (1.6 * 10^-19 )^2/( 5.3 *10^-11)^2
solving for v
v = 2.19*10^6 m/s
let the period of one rotation be T
T = 2*pi*r/v
T = 2 * pi* 5.3 *10^-11/*(2.19*10^6)
T = 1.52 * 10^-16 s
the period of rotation T of the electron is 1.52 * 10^-16 s
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