Question

In a few elements, such as californium, spontaneous fission takes place. The isotope Cf-252 produced artificially by a sequence of neutron absorption, has a half-life of 2.645 y, decaying by alpha emission (96.9%) and spontaneous fission (3.1%). Find the neutron emission rate per gram of Cf252.

Answer 1

The isotope of CF²⁵² has half life of 2.645 years

One could find the decay constant using the relation,

The mass of isotope is 252 g/mole

Using the Avogadros's Number (6.022*10²³), we find the number of atoms/gm of isotope:

Now activity of CF²⁵²/gm:

Since, the probability of Spontaeneous Fission is: 3.1% = 0.031 per decay

and the average number of neutrons produced in spontaeneous fission averages to 3

Therefore, neutron emission rate/gm of CF²⁵²:

Note: The average no of neutrons generated in each fission varies.