The distance of electron from the nucleus in a hydrogen atom is 5x10^-11m.Estimate the electrical potential energy of atom
To estimate the electrical potential energy of an atom, we need to use the formula for electrical potential energy:
Electric potential energy = (k * q1 * q2) / r
Where:
- k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
- q1 and q2 are the charges involved (in this case, the electron and the proton)
- r is the distance between the charges (in this case, the distance of the electron from the nucleus)
In a hydrogen atom, the charge of the electron (q1) is -1.6 x 10^-19 C, and the charge of the proton (q2) is +1.6 x 10^-19 C (these charges have opposite signs).
Given that the distance of the electron from the nucleus (r) is 5 x 10^-11 m, we can now plug these values into the formula:
Electric potential energy = (8.99 x 10^9 N m^2/C^2) * (-1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (5 x 10^-11 m)
Now, let's calculate it:
Electric potential energy = (8.99 x 10^9) * (-1.6 x 10^-19) * (1.6 x 10^-19) / (5 x 10^-11)
Electric potential energy = -4.57 x 10^-18 joules
Therefore, the estimated electrical potential energy of the hydrogen atom is approximately -4.57 x 10^-18 joules. The negative sign indicates that the electron is at a lower potential energy level than when it is at an infinite distance from the nucleus.