Question

A helium 5 decays into helium-4 and neutron. Helium-4 nucleus has a momentum = 1.903 06 × 10–20 N•s & kinetic energy of 2.723 50 × 10–14 J. Helium-4 mass has a mass of 6.64884x10-27 kg and the neutron is 1.67493 x 10-27 kg. What is the mass of helium-5?

Answer 1

It is given that one Helium-5 nucleus at rest decays into one helium-4 nucleus and one neutron, according to the given equation. It is also given that mass defect is seen as increase in kinetic energy.

To find kinetic energy of neutron `KE_n` we use the Law of Conservation of momentum.

`"Initial momentum of He-5 nucleus"=0="Momentum of He-4 nucleus"+"Momentum of neutron"`
`=>"Momentum of He-4 nucleus"=-"Momentum of neutron"`

`-ve` sign shows that both He-4 nucleus and neutron move in the opposite directions.

We know that for neutron

`KE_n=1/2m_n|v_n|^2=p_n^2/(2m_n)`
where `p_n` is momentum of neutron and `m_n` is its mass.

Inserting given values we get

`KE_n=(1.90306xx10^-20)^2/(2xx1.67493xx10^-27)`
`KE_n=1.081130xx10^-13\ J`

Total kinetic energy of both particles`=2.72350xx10^-14+1.081130xx10^-13`
`=1.3534809xx10^-13\ J`

Mass equivalent of this energy `=Deltam=(KE_(Total))/c^2`
where `c=3xx10^8\ ms^-1` is the velocity of light in vacuum.
`=>Deltam=(1.3534809xx10^-13)/(3.xx10^8)^2=1.503867xx10^-30\ kg`

Mass of He-5 nucleus`=6.64884xx10^-27+1.67493 xx 10^-27+1.503867xx10^-30=8.32527xx10^-27\ kg`