The atomic masses of 12 H and 24 H are 2.0141 u and 4.0026 u respectively. Taking the velocity of light in vacuum to be 2.998 × 108 m s -1 , calculate the amount of energy (in J) liberated when two moles of 12 H undergo a fusion to form one mole of 24 H. [ u =1.66057 × 10-27 kg ]

Question

The atomic masses of 12 H and 24 H are 2.0141 u and 4.0026 u respectively. Taking the velocity of light in vacuum to be 2.998 × 108 m s -1 , calculate the amount of energy (in J) liberated when two moles of 12 H undergo a fusion to form one mole of 24 H. [ u =1.66057 × 10-27 kg ] (A) 2.3× 1012J (B) 3.3× 1012J (C) 5.3× 1012J (D) 2.9× 1012J

Tardigrade Admin · Accepted Answer

2 12 H arrow 24 H + Energy Mass defect =2 × 2.0141-4.0026=0.0256 amu beginarrayl ∴ Δ E =Δ m × c 2 =0.0256 × 1.66057 × 10-27 × 6.02 × 1023 ×(2.998 × 108)2 =2.3 × 1012 J endarray

$2.3 \times 1 0^{12} J$

$3.3 \times 1 0^{12} J$

$5.3 \times 1 0^{12} J$

$2.9 \times 1 0^{12} J$

$2_{1}^{2} H \to_{2}^{4} H +$ Energy
Mass defect $= 2 \times 2.0141 - 4.0026 = 0.0256 am u$
$∴ Δ E = Δ m \times c^{2} = 0.0256 \times 1.66057 \times 1 0^{- 27} \times 6.02 \times 1 0^{23} \times (2.998 \times 1 0^{8})^{2} = 2.3 \times 1 0^{12} J$

Q. The atomic masses of 12​H and 24​H are 2.0141u and 4.0026u respectively. Taking the velocity of light in vacuum to be 2.998×108ms−1 , calculate the amount of energy (in J) liberated when two moles of 12​H undergo a fusion to form one mole of 24​H. [u=1.66057×10−27kg]

2.3×1012J

3.3×1012J

5.3×1012J

2.9×1012J

212​H→24​H+ Energy Mass defect =2×2.0141−4.0026=0.0256amu ∴ΔE=Δm×c2=0.0256×1.66057×10−27×6.02×1023×(2.998×108)2=2.3×1012J​

$2.3 \times 1 0^{12} J$

$3.3 \times 1 0^{12} J$

$5.3 \times 1 0^{12} J$

$2.9 \times 1 0^{12} J$

$2_{1}^{2} H \to_{2}^{4} H +$ Energy
Mass defect $= 2 \times 2.0141 - 4.0026 = 0.0256 am u$
$∴ Δ E = Δ m \times c^{2} = 0.0256 \times 1.66057 \times 1 0^{- 27} \times 6.02 \times 1 0^{23} \times (2.998 \times 1 0^{8})^{2} = 2.3 \times 1 0^{12} J$