Question

Under certain circumstances, a nucleus can decay by emitting a particle more massive than an α-particle. Consider the following decay processes:

Calculate the Q-values for these decays and determine that both are energetically allowed.

Answer 1

Take a emission nuclear reaction:

We know that:

Mass of m₁ = 223.01850 u

Mass of m₂ = 208.98107 u

Mass of, m₃ = 14.00324 u

Hence, the Q-value of the reaction is given as:

Q = (m₁ − m₂ − m₃) c²

= (223.01850 − 208.98107 − 14.00324) c²

= (0.03419 c²) u

But 1 u = 931.5 MeV/c²

∴Q = 0.03419 × 931.5

= 31.848 MeV

Hence, the Q-value of the nuclear reaction is 31.848 MeV. Since the value is positive, the reaction is energetically allowed.

Now take a emission nuclear reaction:

We know that:

Mass of m₁ = 223.01850

Mass of m₂ = 219.00948

Mass of, m₃ = 4.00260

Q-value of this nuclear reaction is given as:

Q = (m₁ − m₂ − m₃) c²

= (223.01850 − 219.00948 − 4.00260) C²

= (0.00642 c²) u

= 0.00642 × 931.5 = 5.98 MeV

Hence, the Q value of the second nuclear reaction is 5.98 MeV. Since the value is positive, the reaction is energetically allowed.