Question

hii,
i have been trying to solve this question in forever so help would be much appreciated

A stationary uranium nucleus disintegrates emitting an alpha particle of mass 6.65 × 10^-27 kg and another nucleus X of mass 3.89 × 10 ^-25 kg (they're in opposite direction to one another)

calculate the ratio velocity alpha particle / velocity nucleus X

Answer 1

Answer on Question #72120-Physics-Classical Mechanics

A stationary uranium nucleus disintegrates emitting an alpha particle of mass $6.65 \times 10^{\wedge} - 27\ \mathrm{kg}$ and another nucleus X of mass $3.89 \times 10^{\wedge} - 25\ \mathrm{kg}$ (they're in opposite direction to one another)

Calculate the ratio velocity alpha particle / velocity nucleus X

Solution

$$m_{\alpha} = 6.65 \cdot 10^{-27}\ \mathrm{kg}$$ $$m_{x} = 3.89 \cdot 10^{-25}\ \mathrm{kg}$$

From the conservation of momentum:

$$m_{\alpha} v_{\alpha} = m_{x} v_{x}$$

The ratio velocity alpha particle / velocity nucleus X is

$$\frac{v_{\alpha}}{v_{x}} = \frac{m_{x}}{m_{\alpha}} = \frac{3.89 \cdot 10^{-25}}{6.65 \cdot 10^{-27}} = 58.5$$

Answer: 58.5.

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