Under the action of a given coulombic force the acceleration of an electron is 5.01 × 1022 𝑚/𝑠2.Then, the magnitude of the acceleration of a proton under the action of same force is nearly.Given that mass of proton = 1.67 × 10−27𝑘𝑔; mass of electron = 9.1 × 10−31𝑘𝑔
Question
Under the action of a given coulombic force the acceleration of an electron is 5.01 × 1022 𝑚/𝑠2.Then, the magnitude of the acceleration of a proton under the action of same force is nearly.Given that mass of proton = 1.67 × 10−27𝑘𝑔; mass of electron = 9.1 × 10−31𝑘𝑔
Solution
The acceleration of an object under a force is given by Newton's second law, F = ma, where F is the force, m is the mass of the object, and a is the acceleration.
Given that the electron and the proton are under the same force, we can set up the following equation:
F = me * ae = mp * ap
where me and mp are the masses of the electron and proton respectively, and ae and ap are their accelerations.
We are given that ae = 5.01 × 10^22 m/s^2, me = 9.1 × 10^-31 kg, and mp = 1.67 × 10^-27 kg. We are asked to find ap.
Substituting the given values into the equation, we get:
9.1 × 10^-31 kg * 5.01 × 10^22 m/s^2 = 1.67 × 10^-27 kg * ap
Solving for ap, we get:
ap = (9.1 × 10^-31 kg * 5.01 × 10^22 m/s^2) / (1.67 × 10^-27 kg)
After calculating the above expression, we find that the acceleration of the proton is approximately 2.73 × 10^18 m/s^2.
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