Sol. The splitting reaction of deuteron by a proton may be represented as

P + H 2 — → p + n + p … (1)

The energy of this reaction must be the binding energy of the deuteron. So, the threshold kinetic energy of the proton is given as

T th = |Q|

or, T th = [(m p + m d )/m d ]E b

The proton must have energy T greater than or equal to T th . So, the energy of the proton for the required split reaction is given as

or, Q = {m d – (m p + m n )/m d )}c 2 … (2)

so, E b = |Q|

Now the binding energy of the reaction is given as

E b = [ + (A – Z)m n – m d ]c 2 Since for H

2 , Z = 1 and A = 2. So,

E b = (m p + m n – m d )c 2 … (3)

Here m H is the mass of hydrogen atom. So, m H = m p m n and m d is the masses of neutron and H 2 atom. So, from equations (1) and (3), we get

or,

So, on putting the values, we get