A neutron moving with velocity vn has an inelastic collision with a stationary singly ionized he

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A neutron moving with velocity vn has an inelastic collision...

A neutron moving with velocity $\mathrm{v}_{\mathrm{n}}$ has an inelastic collision with a stationary singly ionized helium ion and both are deflected at $45^{\circ}$ to the original path of the neutron. The helium ion gives out a radiation of $48.36 \mathrm{eV}$ and comes to the ground state. If $\mathrm{v}_{\mathrm{n}}$ ' and $\mathrm{v}_{\mathrm{H}}$ are the final velocities of neutron and helium, (a) $\mathrm{v}_{\mathrm{n}}=\sqrt{2} \mathrm{v}_{\mathrm{n}}$ (b) $\mathrm{v}_{\mathrm{H}}=\frac{\mathrm{v}_{\mathrm{n}}}{4}$ (c) $\mathrm{v}_{\mathrm{H}}=\frac{\mathrm{v}_{\mathrm{n}}}{4 \sqrt{2}}$ (d) If the excited electron gives out more than one radiation instead of a single radiation, the largest possible wavelength is $1643 \AA$.

A neutron moving with velocity $\mathrm{v}_{\mathrm{n}}$ has an inelastic collision with a stationary singly ionized helium ion and both are deflected at $45^{\circ}$ to the original path of the neutron. The helium ion gives out a radiation of $48.36 \mathrm{eV}$ and comes to the ground state. If $\mathrm{v}_{\mathrm{n}}$ ' and $\mathrm{v}_{\mathrm{H}}$ are the final velocities of neutron and helium,
(a) $\mathrm{v}_{\mathrm{n}}=\sqrt{2} \mathrm{v}_{\mathrm{n}}$
(b) $\mathrm{v}_{\mathrm{H}}=\frac{\mathrm{v}_{\mathrm{n}}}{4}$
(c) $\mathrm{v}_{\mathrm{H}}=\frac{\mathrm{v}_{\mathrm{n}}}{4 \sqrt{2}}$
(d) If the excited electron gives out more than one radiation instead of a single radiation, the largest possible wavelength is $1643 \AA$.

Key Concepts

Inelastic Collisions

In an inelastic collision, although overall momentum is conserved, some of the initial kinetic energy is converted into other forms of energy such as internal excitations or radiation. This conversion affects the final speeds of the colliding particles and is a key factor in analyzing energy balance during the collision.

Conservation of Momentum

This principle states that the total momentum of a closed system remains constant if no external forces act on it. In collision problems, momentum must be conserved in every direction, making it essential to analyze vector components especially when deflections, such as 45° angles, are involved.

Conservation of Energy

Energy conservation requires that the sum of all forms of energy in a closed system remains constant. In inelastic collisions, although some energy is radiated away or absorbed in exciting internal states, the total energy—including kinetic, potential, and radiation energies—remains constant, providing a necessary balance for determining unknown speeds or energy losses.

Atomic Energy Transitions

When an atom or ion changes from an excited state to a lower energy state, the excess energy is typically released as radiation. This concept is essential in understanding how radiation emission is connected to the internal energy changes of an atom, especially when multiple photons may be involved.

Photon Energy-Wavelength Relationship

This concept connects the energy of a photon to its wavelength through Planck's relation, where a given amount of energy corresponds to a specific wavelength. This relationship is crucial in determining the characteristics of radiation emitted during energy transitions in atomic systems.

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