We consider the three formation modes, as shown in the figure, for the compound nucleus .

We have to find the energies that (a) particle, (b) the proton, and (c) the gamma-ray photon must have to provide 25.00 MeV of excitation energy to the compound nucleus. Needed atomic masses are

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The atomic number of Ne is 10, so its atom contains 10 electrons.

As the compound nucleus has 25 MeV of excitation energy and in the centre-of-mass frame of the nuclear reaction the compound nucleus will be at rest, therefore the needed total energy must be

For answering this problem, we will use relativistic mechanics. In the collision of two particles of masses and the energy of the particle 1 in the rest frame of particle 2 is given by

(a)

particle

We consider the nuclear reaction

The rest mass energy of an particle will be

The rest mass energy of an nucleus will be

Therefore,

(b)

Proton

We consider the nuclear reaction

The rest mass energy of a proton is

The atomic number of F is 9.

The rest mass energy of a nucleus will be

Therefore,

The kinetic energy of the proton in the laboratory frame will be

(c)

Photon

We consider the nuclear reaction

The rest mass energy of a photon is zero.

The rest mass energy of a nucleus is

Therefore,