We can use Coulomb's law to predict the number of protons in X's nucleus. Coulomb's law states that the force of attraction between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
F = k * (q1 * q2) / r^2
Where F is the force of attraction, k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
We can rearrange the equation to solve for the charge:
q2 = (F * r^2) / (k * q1)
In this case, q1 is the charge on the electron, which is -1.60 x 10^-19 C. The radius of atom X, r, is given, and the force of attraction, F, is also given.
So, we have:
q2 = (2.2 x 10^-8 N * (1.02 x 10^-10 m)^2) / (8.99 x 10^9 Nm^2/C^2 * -1.60 x 10^-19 C)
Solving for q2, we find that q2 = +5.4 x 10^-19 C. This is the charge on the nucleus of atom X. The number of protons in the nucleus of atom X can be found by dividing the charge by the charge of a proton:
N = q2 / qp
Where N is the number of protons and qp is the charge on a proton, which is +1.60 x 10^-19 C.
So, we have:
N = (5.4 x 10^-19 C) / (1.60 x 10^-19 C) = 3.375
Since the number of protons must be a whole number, the closest whole number to 3.375 is 3. This means that atom X has 3 protons in its nucleus. The identity of atom X can be determined based on its atomic number, which is equal to the number of protons in its nucleus. An atomic number of 3 corresponds to the element lithium (Li).