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Under the action of a given coulombic force the acceleration of an electron is 2.5 x 1022 ms-2. Then the magnitude of the acceleration of a proton under the action of same force is nearly
- a)1.6 x 10-19 ms-2
- b)9.1 x 1031 ms-2
- c)1.5 x 1019 ms-2
- d)1.6 x 1027 ms-2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Under the action of a given coulombic force the acceleration of an ele...
The acceleration due to given coulombic force F is
a = (F/m) or a ∝ (1/m) ...(1)
∴
where mc and mp are masses of electron and proton respectively
a = (F/m) or a ∝ (1/m) ...(1)
∴
where mc and mp are masses of electron and proton respectivelyMost Upvoted Answer
Under the action of a given coulombic force the acceleration of an ele...
Given:
- Acceleration of an electron under the action of a coulombic force = 2.5 x 10^22 m/s^2
To find:
Magnitude of the acceleration of a proton under the action of the same force.
Explanation:
The coulombic force experienced by a charged particle is given by Coulomb's law:
F = k * (q1 * q2) / r^2
Where,
F = Force between two charged particles
k = Coulomb's constant (9 x 10^9 Nm^2/C^2)
q1, q2 = Charges of the particles
r = Distance between the particles
The acceleration of a charged particle is given by Newton's second law of motion:
F = m * a
Where,
m = Mass of the particle
a = Acceleration of the particle
Comparing the forces on the electron and the proton:
Since the force is the same for both the electron and the proton, we can equate the coulombic forces on them:
k * (q_e * q_p) / r^2 = k * (q_e * q_e) / r^2
Key point 1:
The charge of an electron (q_e) is -1.6 x 10^-19 C, and the charge of a proton (q_p) is +1.6 x 10^-19 C. Therefore,
-1.6 x 10^-19 * q_p = -1.6 x 10^-19 * -1.6 x 10^-19
Key point 2:
The mass of an electron (m_e) is 9.1 x 10^-31 kg, and the mass of a proton (m_p) is 1.67 x 10^-27 kg.
Substituting the values into the equation:
Using the equation F = m * a, we can solve for the acceleration of the proton:
k * (q_e * q_p) / r^2 = m_p * a_p
Key point 3:
We know that the acceleration of the electron (a_e) is 2.5 x 10^22 m/s^2.
k * (q_e * q_e) / r^2 = m_e * a_e
Solving for a_p:
We can rearrange the equation to solve for the acceleration of the proton:
a_p = (k * (q_e * q_p) / r^2) / m_p
Substituting the values:
Plugging in the given values, we can calculate the acceleration of the proton:
a_p = (9 x 10^9 * (-1.6 x 10^-19 * 1.6 x 10^-19) / r^2) / (1.67 x 10^-27)
Key point 4:
The radius of the orbit (r) is not given, so we cannot calculate the exact value of the acceleration of the proton. However, we can compare it to the acceleration of the electron.
Comparing the accelerations:
Since the magnitude of the charge of the proton is the same as the magnitude of the charge of
- Acceleration of an electron under the action of a coulombic force = 2.5 x 10^22 m/s^2
To find:
Magnitude of the acceleration of a proton under the action of the same force.
Explanation:
The coulombic force experienced by a charged particle is given by Coulomb's law:
F = k * (q1 * q2) / r^2
Where,
F = Force between two charged particles
k = Coulomb's constant (9 x 10^9 Nm^2/C^2)
q1, q2 = Charges of the particles
r = Distance between the particles
The acceleration of a charged particle is given by Newton's second law of motion:
F = m * a
Where,
m = Mass of the particle
a = Acceleration of the particle
Comparing the forces on the electron and the proton:
Since the force is the same for both the electron and the proton, we can equate the coulombic forces on them:
k * (q_e * q_p) / r^2 = k * (q_e * q_e) / r^2
Key point 1:
The charge of an electron (q_e) is -1.6 x 10^-19 C, and the charge of a proton (q_p) is +1.6 x 10^-19 C. Therefore,
-1.6 x 10^-19 * q_p = -1.6 x 10^-19 * -1.6 x 10^-19
Key point 2:
The mass of an electron (m_e) is 9.1 x 10^-31 kg, and the mass of a proton (m_p) is 1.67 x 10^-27 kg.
Substituting the values into the equation:
Using the equation F = m * a, we can solve for the acceleration of the proton:
k * (q_e * q_p) / r^2 = m_p * a_p
Key point 3:
We know that the acceleration of the electron (a_e) is 2.5 x 10^22 m/s^2.
k * (q_e * q_e) / r^2 = m_e * a_e
Solving for a_p:
We can rearrange the equation to solve for the acceleration of the proton:
a_p = (k * (q_e * q_p) / r^2) / m_p
Substituting the values:
Plugging in the given values, we can calculate the acceleration of the proton:
a_p = (9 x 10^9 * (-1.6 x 10^-19 * 1.6 x 10^-19) / r^2) / (1.67 x 10^-27)
Key point 4:
The radius of the orbit (r) is not given, so we cannot calculate the exact value of the acceleration of the proton. However, we can compare it to the acceleration of the electron.
Comparing the accelerations:
Since the magnitude of the charge of the proton is the same as the magnitude of the charge of
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Under the action of a given coulombic force the acceleration of an electron is 2.5 x 1022ms-2. Then the magnitude of the acceleration of a proton under the action of same force is nearlya)1.6 x 10-19 ms-2b)9.1 x 1031 ms-2c)1.5 x 1019ms-2d)1.6 x 1027ms-2Correct answer is option 'C'. Can you explain this answer?
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