An atomic nucleus initially moving at 420m/s emits an alpha particle in the direction of its...

An atomic nucleus initially moving at 420m/s emits an alpha particle in the direction of its velocity, and the new nucleus slows to 346m/s. If the alpha particle has a mass of 2u and the original nucleus has a mass of 222u, what speed does the alpha particle have when it is emitted?

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An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the new nucleus slows to 340 m/s. If the alpha particle has a mass of 2u and the original nucleus has a mass of 220u, what speed does the alpha particle have when it is emitted?

The momentum after the emission of alpha must remain the same after the emission. Since the formula is p=mv, if the mass changes, the speen must change accordingly.

Before, p=mv=420*220=92400kg.m/s

After, you have two particles. The sum of their two momentum must still be 92400kg.m/s

The remaining nucleus has a mass of 218 and a momentum of:
p=mv=218*340=74120 kg.m/s

The alpha particle has a momentum of
92400-74120=18280 kg.m/s
So you can calculate its speed with
v=p/m=18280/2=9140 m/s.
IF THE ALPHA HAD BEEN EMITTED IN THE OTHER DIRECTION, you would have needed to do a vector addition.

genius_generous answered 1 week ago

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