Physics, asked by abcdzyx020700, 1 year ago

A proton of mass m approaches, from a very large distance towards a free proton with a velocity v° along the straight line joining their centres. Find the closest distance of approach between the two protons

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Answered by bishaldasdibru
0

Answer :

The closest distance between two approaching protons can be found using classical mechanics and the inverse square law of electromagnetic force. It is dependent on the mass of the proton and its initial velocity towards the other proton. The exact calculation involves complex mathematical equations, but it is typically in the range of a few femtometers.

Explanation :

The closest distance of approach between two protons can be found using the concept of classical mechanics and the electromagnetic force between two charged particles.

According to Coulomb's law, the force between two point charges is given by:

F = k * q1 * q2 / r^2

where k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

Since the two protons are identical, their electric forces on each other will be equal and opposite, so the net force on either proton will be zero. This means that the two protons will continue to approach each other indefinitely.

However, if we consider the kinetic energy of the proton, it can be seen that as the protons approach each other, their kinetic energy decreases due to the loss of potential energy.

The total energy of the system is conserved, so the decrease in kinetic energy must be equal to the increase in potential energy.

Thus, the closest distance of approach between the two protons will be the distance at which the sum of their kinetic and potential energies is minimized.

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Answered by tiwariakdi
0

Answer:

Hint: At the distance of closest approach, the initial kinetic energy is completely converts into the potential energy of system of protons.

Step 1: Calculate the initial energies of the proton.We assume that initially the protons are at infinite separation.

Hence, initial potential energy can be taken as 0.

The initial kinetic energy is given by K.E.=

21

​ mV

02

​Total initial energy is: E=P.E.+K.E=.=

21mV

02

Step 2: Calculate the distance of closest approach.

At distance of closest approach, the total initial energy is equal to the potential energy of system of protons

P.E=E

⇒ 4πϵ 0

​1de 2

= 2mV 2

 ; where e=charge of proton  and d=distance of closest approach

⇒d= 2πϵ 0

​1mV 0e2

Hence, the distance of closest approach is  

2πϵ 0

mV 02e 2

Explanation:

Hint: At the distance of closest approach, the initial kinetic energy is completely converts into the potential energy of system of protons.

Step 1: Calculate the initial energies of the proton.We assume that initially the protons are at infinite separation.

Hence, initial potential energy can be taken as 0.

The initial kinetic energy is given by K.E.=

21

​ mV

02

​Total initial energy is: E=P.E.+K.E=.=

21mV

02

Step 2: Calculate the distance of closest approach.

At distance of closest approach, the total initial energy is equal to the potential energy of system of protons

P.E=E

⇒ 4πϵ 0

​1de 2

= 2mV 2

 ; where e=charge of proton  and d=distance of closest approach

⇒d= 2πϵ 0

​1mV 0e2

Hence, the distance of closest approach is  

2πϵ 0

mV 02e 2

A proton is a stable subatomic particle, symbol

p, H+, or 1H+ with a positive electric charge of +1 e (elementary charge). Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ratio). Protons and neutrons, each with masses of approximately one atomic mass unit, are jointly referred to as "nucleons" (particles present in atomic nuclei).

One or more protons are present in the nucleus of every atom. They provide the attractive electrostatic central force that binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol Z). Since each element has a unique number of protons, each element has its own unique atomic number, which determines the number of atomic electrons and consequently the chemical characteristics of the element.

The word proton is Greek for "first", and this name was given to the hydrogen nucleus by Ernest Rutherford in 1920. In previous years, Rutherford had discovered that the hydrogen nucleus (known to be the lightest nucleus) could be extracted from the nuclei of nitrogen by atomic collisions.[9] Protons were therefore a candidate to be a fundamental or elementary particle, and hence a building block of nitrogen and all other heavier atomic nuclei.

Although protons were originally considered to be elementary particles, in the mode.

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