Calculate the energy released in joules when one mole of polonium-214 decays according to the following equation21484 po --> 21082 pb + 42 heatomic masses: pb-210 = 209.98284 amu, po-214 = 213.99519 amu, he-4 = 4.00260 amu. (1 kg = 6.022 × 1026 amu; na = 6.022 × 1023 mol–1; c = 2.99792458 × 108 m/s)

ΔE = 8.77 × 10¹¹ J

Explanation:

given,

²¹⁴₈₄Po > ²¹⁰₈₂Pb + 42 He

Atomic masses: Pb-210 = 209.98284 amu

Po-214 = 213.99519 amu

He-4 = 4.00260 amu

1 kg = 6.022 × 10²⁶ amu;

NA = 6.022 × 10²³ mol⁻¹

c = 2.99792458 × 10⁸ m/s

energy of molecule using equation

ΔE = Δm c²

Δm is mass difference and c is speed of light

Δm = 209.98284 + 4.00260 - 213.99519

Δm = - 0.00975 amu

1 amu = 1.66 x 10⁻²⁷ kg

- 0.00975 amu = - 0.00975 x 1.66 x 10⁻²⁷ Kg

                         = -0.016185 x 10⁻²⁷ Kg

total mass = 6.022 × 10²³ x -0.016185 x 10⁻²⁷

                 = -0.097467 x 10⁻⁴ Kg

ΔE = -(0.097467 x 10⁻⁴) (3 x 10^8)²

ΔE = - 8.77 × 10¹¹

ΔE = 8.77 × 10¹¹ J

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