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 occuring electrons is removed. The radius of the orbit is 2.26 × 10-11 m. Determine the magnitude of the electron's centripetal acceleration.

Electron mass= 9.11X 10^-31 kg
Electron charge= -1.60x10^-19 C
Proton charge= 1.60x10^-19 C

Please help!

Electrostatic force=centripetal force Fe=9*10^9*4*(1.6*10^-19)^2/(2.26*10^-11)^2=1.804*10^-6N 1.804*10^-6=9.1*10^-31a a=1.983*10^-24m/s^2

To determine the magnitude of the electron's centripetal acceleration, we can use the formula for centripetal acceleration:

a = (v^2) / r

where:
a is the centripetal acceleration,
v is the velocity of the electron, and
r is the radius of the orbit.

In this case, we don't have the velocity of the electron directly. However, we can use the concept of Coulomb's law to calculate it indirectly.

Since there are only two protons in the nucleus, the electron will experience a force of attraction toward the nucleus due to the electrostatic force between the positively charged protons and the negatively charged electron. The electrostatic force can be calculated using Coulomb's law:

F = (k * |q₁ * q₂|) / r²

where:
F is the force,
k is Coulomb's constant (8.99 × 10^9 Nm²/C²),
|q₁ * q₂| is the product of the magnitudes of the charges (in this case, |q₁ * q₂| = |(-1.60 × 10^-19C) * (+2e)| = 3.20 × 10^-19C),
and r² is the square of the separation distance between the charges.

Since the force acting on the electron is equal to the centripetal force, we can equate the two:

ma = (k * |q₁ * q₂|) / r²

where m is the mass of the electron and a is the centripetal acceleration.

Now, we can solve for the acceleration (a):

a = (k * |q₁ * q₂|) / (m * r²)

Substituting the given values:

m = 9.11 × 10^-31 kg
k = 8.99 × 10^9 Nm²/C²
|q₁ * q₂| = 3.20 × 10^-19C
r = 2.26 × 10^-11 m

a = (8.99 × 10^9 Nm²/C² * 3.20 × 10^-19C) / (9.11 × 10^-31 kg * (2.26 × 10^-11 m)²)

By plugging in the values into the equation and solving it, the magnitude of the electron's centripetal acceleration is approximately 2.29 × 10^22 m/s².