A π0 meson is a sub-atomic particle. A stationary π0 meson, which has mass 2.4 × 10-28 kg, decays to form two γ-ray photons.

Question 9

A π₀ meson is a sub-atomic particle.

A stationary π₀ meson, which has mass 2.4 × 10^-28 kg, decays to form two γ-ray photons.

The nuclear equation for this decay is

π₀ → γ  + γ

(a) Explain why the two γ-ray photons have the same energy. [2]

(b) Determine, for each γ-ray photon,

(i) the energy, in joule, [2]

(ii) the wavelength, [2]

(iii) the momentum. [2]

Reference: Past Exam Paper – June 2010 Paper 41 Q8

Solution:

(a) As a consequence of the conservation of momentum, the momenta of the photons must be equal and opposite. Since the photons have the same momenta, they must then have the same energy.

(b)

(i)

{We need to calculate the energy of a single photon.

Mass = 1.2×10^-28 kg

Einstein’s mass-energy relation:}

(Δ)E = (Δ)mc²                                            

(Δ)E = 1.2×10^-28 × (3.0×10⁸)²

(Δ)E = 1.08×10^-11 J            

(ii)

E = hc / λ

{λ = hc / E}

λ = (6.63×10^-34 × 3.0×10⁸) / (1.08×10^-11)          

λ = 1.84×10^-14 m                                          

(iii)

{de Broglie wavelength:}

λ = h / p

p = (6.63×10^-34) / (1.84×10^-14)

p = 3.6×10^-20 N s