Obtain the maximum kinetic energy of β-particles, and the radiation frequencies of γ decay in the decay scheme shown in Fig. 13.6. You are given that

m(¹⁹⁸Au) = 197.968233 u

m(¹⁹⁸Hg) = 197.966760 u

From the given diagram γ₁ decays from the 1.088 MeV energy level to 0 MeV level.

We have,

E = hν

Where,

h = plank’s constant = 6.6×10^-34 J s

ν = frequency

Thus, frequency of radiation radiated by γ₁ decay is given by,

(∵ 1 eV = 1.6×10^-19 C )

Thus, frequency of radiation radiated by γ₂ decay is given by,

(∵ 1 eV = 1.6×10^-19 C )

Thus, frequency of radiation radiated by γ₃ decay is given by,

(∵ 1 eV = 1.6×10^-19 C )

Given,

Mass of , m₁ = 2.014102 u

Mass of , m₂ = 3.016049 u

The energy of the highest level is given by,

Where,

Δm = Mass defect (or) mass lost during reaction

c = speed of light

∴ E = (197.968233 – 197.966760) u×c²

= 0.001473 u×931.5 MeV/c²

= 1.3720995 MeV

Since, β₁ decays from maximum level to 1.088 MeV level then,

Kinetic energy of the β₁ particle = (1.3720995 – 1.088) MeV

= 0.2840995 MeV

Since, β₂ decays from maximum level to 0.412 MeV level then,

Kinetic energy of the β₂ particle = (1.3720995 – 0.412) MeV

= 0.9600995 MeV