# Momentum - related question

#1
I have been trying to solve this problem for quite a while now, I even asked one of my teachers and they found it hard and could not solve it.
So,

A stationary unstable nucleus of mass M emits an alpha particle of mass m with kinetic energy E .

What is the speed of recoil of the daughter nucleus ?

A ) √2mE / (M-m)

I've attached a photo of the question so you also see the diagram, maybe it helps.
( https://imgur.com/8UbT5Jg )
But I do not know how to get to it. Can anyone explain it step by step please? Thank you !
0
1 year ago
#2
Attachment 971332

I got this far, but I don’t know how they get the m on the top of the fraction, maybe you could work it out from here?
1
1 year ago
#3
(Original post by Thanquinho)
I have been trying to solve this problem for quite a while now, I even asked one of my teachers and they found it hard and could not solve it.
So,

A stationary unstable nucleus of mass M emits an alpha particle of mass m with kinetic energy E .

What is the speed of recoil of the daughter nucleus ?

A ) √2mE / (M-m)

I've attached a photo of the question so you also see the diagram, maybe it helps.
( https://imgur.com/8UbT5Jg )
But I do not know how to get to it. Can anyone explain it step by step please? Thank you !

Alpha particle has mass m and kinetic energy E, so if it's speed is u, then we have

And we can rearrange to get .....(1)

Mass of daughter nucleus is M-m, and let it's speed be v.

Then by conservation of momentum.

Make v the subject and substitute for u from (1)
1
#4
(Original post by RoseVet)
Attachment 971332

I got this far, but I don’t know how they get the m on the top of the fraction, maybe you could work it out from here?
Thanks !
0
#5
(Original post by ghostwalker)
Alpha particle has mass m and kinetic energy E, so if it's speed is u, then we have

And we can rearrange to get .....(1)

Mass of daughter nucleus is M-m, and let it's speed be v.

Then by conservation of momentum.

Make v the subject and substitute for u from (1)
Thank you, I ve asked about 3 teachers and all of them got stuck on this question.
0
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