The carbon isotope 14C is used for carbon dating of objects. A 14C nucleus can change into a different kind of element, a neighbor on the periodic table with lower mass, by emitting a beta particle – an electron or positron – plus a neutrino or an anti-neutrino. Consider the scenario where 14C ( mass of 2.34 x 10 -26) decays by emitting an electron and anti neutrino. The electron has a mass of 9.11x 10-31 kg and a speed of 4.0 x107 m/s. While the anti neutrino has a momentum of 4.0x10-24 kg-m/s. If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.
5 answers
The scientific notations should say 2.34 x 10^-26; 9.11 x 10^-31; 4.0 x 10^7; 4.0 x 10^-24; sorry about that.
momentum of electron: mv=9.11E-31 *4.0E7
=3.64400e-23kg-m/s
Momentum of neutrino:4.0x10-24 kg-m/s
these are right triangles
momentumNucleus^2= sume of above squared
= (4.0E-24)^2 + (3.64400e-23)^2 =1.3438736e-45
speed nuceuls= sqrt(above) / massNucleus
= 3.66588816e-23 / 2.34 E-26 = 1567 m/s
check all that
=3.64400e-23kg-m/s
Momentum of neutrino:4.0x10-24 kg-m/s
these are right triangles
momentumNucleus^2= sume of above squared
= (4.0E-24)^2 + (3.64400e-23)^2 =1.3438736e-45
speed nuceuls= sqrt(above) / massNucleus
= 3.66588816e-23 / 2.34 E-26 = 1567 m/s
check all that
momentum of electron (say in x direction)
Px = 9.11*10^-31 ( 4*10^7 ) = 36.44 * 10^-24
momentum of anti-n (say in y direction)
Py = 4*10^-24
|P| =sqrt( Px^2+Py^2)
= 10^-24 sqrt( 36.44^2 + 16)
= 36.7 * 10^-24
so
m v = 36.7*10^-24
2.34 * 10^-26 v = 36.7 * 10^-24
v = 15.7 * 10^2
v = 1570 m/s
Px = 9.11*10^-31 ( 4*10^7 ) = 36.44 * 10^-24
momentum of anti-n (say in y direction)
Py = 4*10^-24
|P| =sqrt( Px^2+Py^2)
= 10^-24 sqrt( 36.44^2 + 16)
= 36.7 * 10^-24
so
m v = 36.7*10^-24
2.34 * 10^-26 v = 36.7 * 10^-24
v = 15.7 * 10^2
v = 1570 m/s
whew, we agree :)
Many thanks!