A hydrogen atom is made of a proton (mP = 1.67Ý10-27 kg) as a nucleus and an ele

Question

A hydrogen atom is made of a proton (mP = 1.67Ý10-27 kg) as a nucleus and an electron circling around. In the Bohr model of atoms, the radius of an hydrogen atom is the Bohr radius (5.3Ý10-11 m).

A.) Calculate the gravitational force between the nucleus and electron.

B.) Calculate the electric force between the nucleus and electron.

C.) Assuming that the centrifugal force force of the electron's rotational motion is the same as the electric force, calculate the linear velocity of the electron in a hydrogen atom.

Explanation / Answer

m=1.67*10^-27 Kg

r=5.38*10^-11 m

F gravitatonal= Gm1m2/r^2

F=(6.67*10^-11*1.67*10^-27*9.11*10^-31)/(28.09*1^-22)

F=3.61 * 10^-20 N

B)F electrical =kq1*q2/r^2

F=-(9*10^9*1.6*1.6*10^-38)/(28.09*10^-22)
F=-0.82 *10^-16 N

C)F= m*v^2 / r
0.82 *10^-16*r/m = v^2
v^2= (0.82*5.38*10^-11*10^-16)/(1.67*10^-27 )
v^2=2.64
v=1.625 m/s

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