Question

An electron is held up against the force of gravity by the attraction of a fixed proton some distance above it. How far above the electron is the proton

Answer 1

5.08 m

Step-by-step explanation:

The weight of the electron is being counteracted by the attractive electrostatic force exerted by the proton above it. We can write the force equation as follows:

`m_eg = k_e(Q_pQ_e)/(r^2)`

where the Q's are the charges of the proton and electron, r is the distance between the particles, g is the acceleration due to gravity,
`m_e` is the mass of the electrons and
`k_e` is the Coulomb constant. So solving for r, we get

`r^2 = k_e(Q_pQ_e)/(m_eg)`

Taking the square root of r^2, we then get the distance as

`r = \sqrt{k_e(Q_pQ_e)/(m_eg)}`

The values are given as follows:

`m_e = 9.11×10^(-31)\:\text{kg}`

`g = 9.8\:\text{m/s}^2`

`Q_p = Q_e = 1.60×10^(-19)\:\text{C}`

`k_e = 8.99×10^9\:\text{N-m}^2\text{/C}^2`

Putting in all of these values in our equation for r,

`r = \sqrt{\frac{(8.99×10^9\:\text{N-m}^2\text{/C}^2)(1.60×10^(-19)\:\text{C})^2}{(9.11×10^(-31)\:\text{kg})(9.8\:\text{m/s}^2)}}`

`\:\:\:\:\:= 5.08\:\text{m}`