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In a Rutherford scattering experiment when a projectile of charge z1 and mass M1 approaches a target nucleus of charge z2 and mass M2, the distance of closest approach is r0. The energy of the projectile is:
- a)directly proportional to z1 z2
- b)inversely proportional to z1
- c)directly proportional to mass M1
- d)directly proportional to M1 x M2
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
Rutherford scattering is a phenomenon where a projectile of charge z1 and mass M1 is scattered by a target nucleus of charge z2 and mass M2. The distance of closest approach during the scattering is known as r0.
The energy of the projectile is directly proportional to z1 z2. This is because the energy of the projectile is related to the electrostatic potential energy between the projectile and the target nucleus. The electrostatic potential energy is given by the equation:
U = (z1 z2 e^2) / (4πε0 r)
where e is the elementary charge and ε0 is the permittivity of free space. As the distance between the projectile and the target nucleus decreases, the electrostatic potential energy increases. Therefore, the energy of the projectile is directly proportional to z1 z2.
Option A is the correct answer as it states that the energy of the projectile is directly proportional to z1 z2.
Other options are incorrect because:
- Option B is incorrect because the energy of the projectile is not inversely proportional to z1. The charge of the projectile affects the electrostatic potential energy, which is directly proportional to z1 z2.
- Option C is incorrect because the energy of the projectile is not directly proportional to mass M1. The mass of the projectile affects the kinetic energy of the projectile, but not the electrostatic potential energy.
- Option D is incorrect because the energy of the projectile is not directly proportional to M1 x M2. The masses of the projectile and the target nucleus affect the kinetic energy of the projectile, but not the electrostatic potential energy.
Rutherford scattering is a phenomenon where a projectile of charge z1 and mass M1 is scattered by a target nucleus of charge z2 and mass M2. The distance of closest approach during the scattering is known as r0.
The energy of the projectile is directly proportional to z1 z2. This is because the energy of the projectile is related to the electrostatic potential energy between the projectile and the target nucleus. The electrostatic potential energy is given by the equation:
U = (z1 z2 e^2) / (4πε0 r)
where e is the elementary charge and ε0 is the permittivity of free space. As the distance between the projectile and the target nucleus decreases, the electrostatic potential energy increases. Therefore, the energy of the projectile is directly proportional to z1 z2.
Option A is the correct answer as it states that the energy of the projectile is directly proportional to z1 z2.
Other options are incorrect because:
- Option B is incorrect because the energy of the projectile is not inversely proportional to z1. The charge of the projectile affects the electrostatic potential energy, which is directly proportional to z1 z2.
- Option C is incorrect because the energy of the projectile is not directly proportional to mass M1. The mass of the projectile affects the kinetic energy of the projectile, but not the electrostatic potential energy.
- Option D is incorrect because the energy of the projectile is not directly proportional to M1 x M2. The masses of the projectile and the target nucleus affect the kinetic energy of the projectile, but not the electrostatic potential energy.
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In a Rutherford scattering experiment when a projectile of charge z1 and mass M1 approaches a target nucleus of charge z2 and mass M2, the distance of closest approach is r0. The energy of the projectile is:a)directly proportional to z1 z2b)inversely proportional to z1c)directly proportional to mass M1d)directly proportional to M1 x M2Correct answer is option 'A'. Can you explain this answer?
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