Atomic Collision

Atomic collisions refer to the interactions between atoms or subatomic particles that result in the transfer of energy, momentum, or charge. These collisions are fundamental to understanding various physical and chemical processes, from the behaviour of gases to nuclear reactions. In real life, atomic collisions play a crucial role in technologies like particle accelerators, which probe the structure of matter, and in medical applications such as radiation therapy for cancer treatment. Understanding atomic collisions also aids in the development of more efficient energy sources and better materials through insights gained at the atomic level. This article delves into the mechanisms and significance of atomic collisions in both scientific and practical contexts.

Atomic Collision

Atomic collisions refer to the interactions between atoms or subatomic particles that result in the exchange of energy, momentum, or charge. These collisions are pivotal in understanding various physical and chemical processes, influencing the behaviour of gases, the principles of spectroscopy, and the dynamics of nuclear reactions. In real life, atomic collisions are essential in technologies like particle accelerators, which delve into the structure of matter, and in medical applications such as radiation therapy for treating cancer

There are two ways to excite an electron in an atom

1. By supplying energy to an electron through electromagnetic photons for eg., the Photoelectric effect

2. By the atomic collision, the kinetic energy loss is utilized in the ionization or excitation of the atom.

Now let us understand the atomic collision

Collision of a Neutron with an Atom

The collision of a neutron with an atom is a fundamental process in nuclear physics and has significant implications in various fields. When a neutron collides with an atom, it can result in several outcomes depending on the energy of the neutron and the type of atom it encounters. These outcomes include elastic scattering, where the neutron bounces off the nucleus, transferring some of its energy to the atom, and inelastic scattering, where the neutron is absorbed, leading to the emission of gamma rays or other particles.

Let us consider an example of a head-on collision of a moving neutron with a stationary hydrogen atom as shown in the figure. Here. for mathematical analysis, let us assume the masses of the neutron and H atom to be the same

Now there are two cases, the first is a perfectly elastic collision and another is a perfectly inelastic collision. Let us discuss these cases one by one -

1. Perfect Elastic collision

A perfectly elastic collision is a type of collision in which both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system remain the same before and after the collision. In such collisions, the objects involved rebound off each other without any loss of energy due to sound, heat, or deformation.

In this case, since the mass of the neutron and the mass of the hydrogen atom, then the hydrogen atom will move with the same speed and kinetic energy as which neutron is moving initially.

2. Perfect Inelastic collision

A perfect inelastic collision is a type of collision in which the colliding objects stick together after impact, resulting in a single combined mass moving with a common velocity. In such collisions, momentum is conserved, but kinetic energy is not. The loss of kinetic energy is converted into other forms of energy, such as heat, sound, or deformation.

If both have perfect inelastic collision, then both move together. Now by applying the conservation of momentum

mv0=2mv1⇒v1=v2

vo is the initial velocity of the neutron
v1 is the final combined velocity of the atom and neutron.

Now the difference between initial and final kinetic energy is given as -

ΔE=Ei−Ef=12mvo2−12(2m)(vo2)2=12mvo2−14mvo2=14mvo2=12Ei

Thus, half of the initial kinetic energy will be lost in the collision. The energy lost can only be absorbed by the atom involved in the collision and may get excited or ionized by this energy loss which takes place in case of inelastic collision. Here we are not considering the heat energy loss during the collision.

This loss in energy can be absorbed by the H atom only. From the previous concepts, we know that the minimum energy needed by the hydrogen atom to get excited is 10.2 eV for n =1 to n=2. So the minimum energy loss must be equal to 10.2 eV to excite hydrogen atoms. If the loss in energy is more than 10.2 eV then only 10.2 eV is absorbed by the hydrogen atom and the rest of the energy remains in the colliding particles (Neutron and H atom) as the collision is not perfectly inelastic.

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Solved Examples Based on Atomic Collision

Example 1: An electron with kinetic energy E eV collides with a hydrogen atom in the ground state. The collision is observed to be elastic for:

1) 0<E<∞
2) 0<E<10.2eV
3) 0<E<13.6eV
4) 0<E<3.4eV

Solution

The hydrogen atom in the ground state will only absorb energy greater than 10.2eV. When an electron with KE, E eV collides with a hydrogen atom in the ground state, if the energy of an electron is absorbed then the collision will be inelastic. If there is no absorption of energy(i.e. E<10.2eV) then the collision will be elastic.

Hence, the answer is the option (2)

Example 2: A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is?

1) 16/82

2) 8/9

3) 2/3

4) 8/27

Solution:

Velocity of neutron and deutronV1 2 where Md= mass of deutron Mn= mass of neutronv v2=2 mnmn+md

∵md=2ne Hencev 2=23vv1=13 V= velocity of neutron before collision

Kinetic energy before collision of neutron (E)v2=23vv1=13 kinetic energy after collision (E1)

=12Mnv12=12(19Mnv2) Fractional loss =E−E1E=12Mn(v2−19v2)12Mnv2=89

Hence, the answer is the option (2).

Example 3: A particle of mass 200MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV)

is N4. The value of N is . (Given the mass of the hydrogen atom to be 1GeV/c2)

1) 51

2) 102

3) 204

4) 408

Solution:

M0=200MeV/c2;m=1GeV/c2 Initial velocity =v0Mv0=mv∴v=(Mm)v012Mv02=12mv2+ΔE0×34(ΔE0=13.6eV)⇒12Mv02(1−Mm)=34ΔE0⇒12Mv02=34×ΔE0×108=14(3ΔE0×108)=514=514eV∴N=51

Hence, the answer is the option (1).

Example 4: A neutron strikes a stationary H-atom in its ground state. If the collision is perfectly inelastic then which of the following kinetic energy of a neutron is not possible?

1) 20.4eV

2) 22.8eV

3) 24.18eV

4) 25.5eV

Solution:

Perfectly Inelastic Collision

This can happen when K.E. of neutron = 20.4 ev, 24.18 ev, 25.5 ev,26.18 ev

wherein

The energy exchanged is exactly half of K.E.of neutron

For a perfectly inelastic collision, the KE of the neutron should be equal to twice the energy gap between ant two orbitals of the hydrogen atom.

20.4=2(ΔE1−2)24.18=2(ΔE1−3)25.5=2(ΔE1−4)

Hence, the answer is the option (2).

Example 5: Two hydrogen atoms in the ground state collide inelastically. The maximum amount by which their combined kinetic energy is reduced is:

1) 10.2 eV

2) 20.4 eV

3) 13.6 eV

4) 27.2 eV

Solution:

The initial kinetic energy of each of the two hydrogen atoms in the ground state =13.6eV

The kinetic energy of both H atoms before the collision =2×13.6eV=27.2eV

As the collision is inelastic, linear momentum is conserved but some kinetic energy is lost.

If one H atom goes to the first excited state and the other remains in the ground state, then their combined kinetic energy after the collision

=13.622eV+13.6eV=17eV

Reduction in their combined kinetic energy =27.2eV−17eV=10.2eV

Hence, the answer is the option (1).

Summary

Atomic collisions involve the interaction of atoms or subatomic particles, resulting in the exchange of energy, momentum, or charge. These collisions, which can be either elastic or inelastic, are crucial for understanding physical and chemical processes. Inelastic collisions, where the objects stick together, result in a loss of kinetic energy that may excite or ionize the atoms involved. Real-life applications include nuclear reactions, particle accelerators, and radiation therapy. Solving problems related to atomic collisions helps in understanding energy conservation, energy transfer, and the resulting changes in atomic states.