Question

Multiple-Concept Example 3 provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 2.99 × 10-11 m. Determine the magnitude of the electron's centripetal acceleration.

Answer 1

Electron's centripetal acceleration,
`a=5.66* 10^(23)\ m/s^2`

Step-by-step explanation:

Given that,

The radius of the orbit,
`r=2.99* 10^(-11)\ m`

The centripetal force is balanced by the electrostatic force such that,

`k(q_1q_2)/(r^2)=(mv^2)/(r)`

`a=(v^2)/(r)=(kq_1q_2)/(mr^2)`

Here,
`q_1=e` and
`q_2=2e`

`a=(9* 10^9* 1.6* 10^(-19)* 2* 1.6* 10^(-19))/(9.1* 10^(-31)* (2.99* 10^(-11))^2)`

`a=5.66* 10^(23)\ m/s^2`

So, the magnitude of the electron's centripetal acceleration
`5.66* 10^(23)\ m/s^2`. Hence, this is the required solution.