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15 points! An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m/s. If the alpha particle has a mass of 4.0 u and the original nucleus had a mass of 222 u, what speed does the alpha particle have when it is emitted?

Use conservation of momentum to solve.

Respuesta :

skyluke89

The alpha particle is emitted at 4235 m/s

Explanation:

We can use the law of conservation of momentum to solve the problem: the total momentum of the original nucleus must be equal to the total momentum after the alpha particle has been emitted. Therefore:

[tex]p_i = p_f\\ Mu=m_1 v_1 + m_2 v_2 =[/tex]  

where:  

[tex]M =222u [/tex] is the mass of the original nucleus

[tex]v=420 m/s[/tex] is the initial velocity of the nucleus

[tex]m_1 = 4 u[/tex] is the mass of the alpha particle

[tex]v_1[/tex] is the final velocity of the alpha particle

[tex]m_2 = 222u-4u = 218 u[/tex] is the mass of the daughter nucleus

[tex]v_2 = 350 m/s[/tex] is the final velocity of the nucleus

Solving for [tex]v_1[/tex], we  find the final velocity of the alpha particle:

[tex]v_1 = \frac{Mu-m_2 v_2}{m_1}=\frac{(222)(420)-(218)(350)}{4}=4235 m/s[/tex]

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