The distance between the proton and the electron in a deuterium atom is 51.0 pm. The strength of the electric field due to the proton at this position of the electron is
The strength of the electric field due to the proton at the position of the electron can be calculated using Coulomb's law:
Electric field = (k * Q) / r^2
Where:
- k is the electrostatic constant, approximately 8.99 × 10^9 N m^2/C^2
- Q is the charge of the proton, approximately 1.6 × 10^-19 C
- r is the distance between the proton and the electron, 51.0 pm (1 pm = 1 × 10^-12 m)
Plugging in the values:
Electric field = (8.99 × 10^9 N m^2/C^2 * 1.6 × 10^-19 C) / (51.0 × 10^-12 m)^2
Simplifying:
Electric field = (8.99 × 1.6) / (51.0)^2 * 10^(9-19+12) N/C
Electric field = 0.28 × 10^2 N/C
Electric field = 2.8 N/C
Therefore, the strength of the electric field due to the proton at the position of the electron is 2.8 N/C.
To calculate the strength of the electric field due to the proton at the position of the electron, we can use the equation for electric field strength:
Electric field strength (E) = Coulomb's constant (k) * charge (q) / distance (r)^2
In this case, the charge of the proton and electron is the same (e = 1.6 x 10^-19 C), and the distance between them is given as 51.0 pm = 51.0 x 10^-12 m.
The value of Coulomb's constant (k) is 8.99 x 10^9 Nm^2/C^2.
Plugging these values into the equation, we get:
E = (8.99 x 10^9 Nm^2/C^2) * (1.6 x 10^-19 C) / (51.0 x 10^-12 m)^2
Simplifying the equation gives:
E = (8.99 x 1.6) / (51.0)^2 N/C
Calculating further, we get:
E = 0.2817666... N/C
Therefore, the strength of the electric field due to the proton at the position of the electron in a deuterium atom is approximately 0.28 N/C.
To find the strength of the electric field due to the proton at the position of the electron in a deuterium atom, we can use Coulomb's law.
Coulomb's law states that the electric field strength (E) generated by a point charge is given by the equation:
E = k * (Q / r^2)
Where:
- E is the electric field strength
- k is the electrostatic constant (9.0 x 10^9 Nm^2/C^2)
- Q is the charge of the point charge
- r is the distance between the point charge and the position where the electric field is measured.
In this case, the charge of a proton is equal to +1.6 x 10^-19 C, and the distance between the proton and the electron is given as 51.0 pm (where 1 pm = 1 x 10^-12 m).
First, we need to convert the given distance from picometers (pm) to meters (m):
51.0 pm = 51.0 x 10^-12 m
Now, we can calculate the electric field strength:
E = (9.0 x 10^9 Nm^2/C^2) * [(+1.6 x 10^-19 C) / (51.0 x 10^-12 m)^2]
Simplifying the equation and performing the calculations yields:
E = 3,160 N/C (rounded to three significant figures)
Therefore, the strength of the electric field due to the proton at the position of the electron in a deuterium atom is 3,160 N/C.