A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

  • Option 1)

    The helium nucleus has less momentum than the thorium nucleus.

  • Option 2)

    The helium nucleus has more momentum than the thorium nucleus.

  • Option 3)

    The helium nucleus has less kinetic energy than the thorium nucleus.

  • Option 4)

    The helium nucleus has more kinetic energy than the thorium nucleus.

 

Answers (1)

As we learnt

? -decay -

^{A}_{Z}X
ightarrow ^{A-4}_{Z-2}Y+^{4}_{2}He+Q

 

- wherein

Q: value = left ( M_{X} -M_{Y}-M_{He}
ight )c^{2}

 

 \bigcup_{92}^{238}\rightarrow _{90}^{234}\textrm{Th}+_{2}^{4}\textrm{He}

Since from conservation of momentum, momentum of Thorium and Helium is same. Hence kinetic energy of Helium will be greater than kinetic energy of thorium.

\left | \vec{p_{Th}} \right |= \left | \vec{p_{He}} \right |= p

K.Eth = p2/2mth; K.EHe=p/2mHe

\because m_{He}<m_{th}

\therefore K.E_{He}>K.E_{th}


Option 1)

The helium nucleus has less momentum than the thorium nucleus.

this is incorrect option

Option 2)

The helium nucleus has more momentum than the thorium nucleus.

this is incorrect option

Option 3)

The helium nucleus has less kinetic energy than the thorium nucleus.

this is incorrect option

Option 4)

The helium nucleus has more kinetic energy than the thorium nucleus.

this is correct option

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