In a nuclear fission reaction of an isotope of mass M three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect will be

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Q.
In a nuclear fission reaction of an isotope of mass M three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $∆ M$ will be [2024]

1 $\sqrt{\frac{2 c Δ M}{M}}$

2 $\frac{Δ M c^{2}}{3}$

3 $c \sqrt{\frac{2 Δ M}{M}}$

4 $c \sqrt{\frac{3 Δ M}{M}}$

Ans.
(3)

$M = 3 m$

$Δ K . E . = energy released due to fission$

$3 (\frac{1}{2} m v^{2}) = Δ M C^{2}$

$\frac{3}{2} m v^{2} = Δ M C^{2}$

$v^{2} = \frac{2 Δ M C^{2}}{M}$

$v = \sqrt{\frac{2 Δ M C^{2}}{M}} = C \sqrt{\frac{2 Δ M}{M}}$

Solution

Q.
In a nuclear fission reaction of an isotope of mass M three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $∆ M$ will be [2024]

1 $\sqrt{\frac{2 c Δ M}{M}}$

2 $\frac{Δ M c^{2}}{3}$

3 $c \sqrt{\frac{2 Δ M}{M}}$

4 $c \sqrt{\frac{3 Δ M}{M}}$

Ans.
(3)

$M = 3 m$

$Δ K . E . = energy released due to fission$

$3 (\frac{1}{2} m v^{2}) = Δ M C^{2}$

$\frac{3}{2} m v^{2} = Δ M C^{2}$

$v^{2} = \frac{2 Δ M C^{2}}{M}$

$v = \sqrt{\frac{2 Δ M C^{2}}{M}} = C \sqrt{\frac{2 Δ M}{M}}$

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Solution

Q. In a nuclear fission reaction of an isotope of mass M three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect ∆M will be [2024]

1 2cΔMM

2 ΔMc23

3 c2ΔMM

4 c3ΔMM

Ans. (3) M=3m ΔK.E.=energy released due to fission 3(12mv2)=ΔMC2 32mv2=ΔMC2 v2=2ΔMC2M v=2ΔMC2M=C2ΔMM

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Q.
In a nuclear fission reaction of an isotope of mass M three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $∆ M$ will be [2024]

1 $\sqrt{\frac{2 c Δ M}{M}}$

2 $\frac{Δ M c^{2}}{3}$

3 $c \sqrt{\frac{2 Δ M}{M}}$

4 $c \sqrt{\frac{3 Δ M}{M}}$

Ans.
(3)

$M = 3 m$

$Δ K . E . = energy released due to fission$

$3 (\frac{1}{2} m v^{2}) = Δ M C^{2}$

$\frac{3}{2} m v^{2} = Δ M C^{2}$

$v^{2} = \frac{2 Δ M C^{2}}{M}$

$v = \sqrt{\frac{2 Δ M C^{2}}{M}} = C \sqrt{\frac{2 Δ M}{M}}$