(a) Draw the energy level diagram showing the emission of $\beta$-particles followed by $\gamma$-rays by a $^{60}_{27}\mathrm{Co}$ nucleus. (b) Plot the distribution of kinetic energy of $\beta$-particles and state why the energy spectrum is continuous.

Co-60 $\to$ Ni-60 by $\beta^-$ then two $\gamma$; spectrum continuous (energy shared with antineutrino).

CBSE Class 12 · 2005 · All India · Modern PhysicsShort Answer

(a) Draw the energy level diagram showing the emission of

β

-particles followed by

γ

-rays by a

_{27}^{60} Co

nucleus.
(b) Plot the distribution of kinetic energy of

β

-particles and state why the energy spectrum is continuous.

Answer: Co-60 $\to$ Ni-60 by $β^{-}$ then two $γ$ ; spectrum continuous (energy shared with antineutrino).

Solution

(a)

_{27}^{60} Co

decays by

β^{-}

emission to an excited state of

_{28}^{60} Ni

, which then de-excites by emitting two

γ

-rays of

1.17 MeV

and

1.33 MeV

to reach the ground state (see energy-level diagram).
(b) The kinetic-energy distribution of the

β

-particles is continuous, extending from zero up to a definite maximum

K_{ma x}

(see graph).
It is continuous because in

β

-decay the available energy is shared among three products — the daughter nucleus, the electron and the antineutrino — in continuously varying proportions, so the electron can carry any energy from

0

K_{ma x}

Energy shared with the (anti)neutrino \Rightarrow continuous β -spectrum

CBSE Class 12 Board · 2005 · All India · Subjective

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CBSE Class 12 · 2005 · All India · Modern PhysicsShort Answer

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