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?

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1 Answer
A08
Mar 15, 2018

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#

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