The binding energies per nucleon for a deuteron and an α-particle are x1 and x 2 respectively. The energy Q released in the reaction 2 H 1+ 2 H 1 arrow 4 He 2+Q, is

Question

The binding energies per nucleon for a deuteron and an α-particle are x1 and x 2 respectively. The energy Q released in the reaction 2 H 1+ 2 H 1 arrow 4 He 2+Q, is (A) 4(x1+x2) (B) 4(x2-x1) (C) 2(x2-x1) (D) 2(x1 + x2)

Tardigrade Admin · Accepted Answer

Number of nucleon on reactant side =4 Binding energy for one nucleon =x1 Binding energy for 4 nucleons =4 x1, Similarly on product side binding energy =4 x2 Now, Q = change in binding energy =4(x2-x1).

Q. The binding energies per nucleon for a deuteron and an $α$ -particle are $x_{1}$ and $x_{2}$ respectively. The energy $Q$ released in the reaction $^{2} H_{1} +^{2} H_{1} \to^{4} H e_{2} + Q$ , is

$4 (x_{1} + x_{2})$

$4 (x_{2} - x_{1})$

$2 (x_{2} - x_{1})$

$2 (x_{1} + x_{2})$

Number of nucleon on reactant side $= 4$
Binding energy for one nucleon $= x_{1}$
Binding energy for $4$ nucleons $= 4 x_{1}$ ,
Similarly on product side binding energy $= 4 x_{2}$
Now, $Q =$ change in binding energy $= 4 (x_{2} - x_{1})$ .

Q. The binding energies per nucleon for a deuteron and an α-particle are x1​ and x2​ respectively. The energy Q released in the reaction 2H1​+2H1​→4He2​+Q, is

4(x1​+x2​)

4(x2​−x1​)

2(x2​−x1​)

2(x1​+x2​)