Fundamental Particles - Meson Decay Question

[Magda|A380]

Homework Statement

The pion-zero meson has its mass quoted as 135.0MeV/c².
It decays into two gamma rays:
∏⁰ → γ + γ
b) Assuming the ∏⁰meson to be initially at rest, calculate the energy and hence the wavelength of the two gamma rays.

Homework Equations

E= hc/λ

The Attempt at a Solution

Part a) just wanted me to calculate the mass in kg; which was fine, but I'm having trouble with part b).
E = 135.0 MeV, which I get to be 2.16x10^-11J
I halved this value as there are two gamma rays, to get 1.08x10^-11J
Using this value for E in the equation E=hc/λ, my value for λ is 1.84x10^-14; however according to my book the answer should be 1.98x10^-14
Could someone please tell me where I'm going wrong?
Thank you

 

[collinsmark]

Hello Magda|A380,

Welcome to Physics Forums!

Homework Statement

The pion-zero meson has its mass quoted as 135.0MeV/c².
It decays into two gamma rays:
∏⁰ → γ + γ
b) Assuming the ∏⁰meson to be initially at rest, calculate the energy and hence the wavelength of the two gamma rays.

Homework Equations

E= hc/λ

The Attempt at a Solution

Part a) just wanted me to calculate the mass in kg; which was fine, but I'm having trouble with part b).
E = 135.0 MeV, which I get to be 2.16x10^-11J
I halved this value as there are two gamma rays, to get 1.08x10^-11J
Using this value for E in the equation E=hc/λ, my value for λ is 1.84x10^-14; however according to my book the answer should be 1.98x10^-14
Could someone please tell me where I'm going wrong?
Thank you

For what it's worth, I calculated the same answer that you did (λ = 1.84 x 10^-14 m, to three significant figures).

 

[Magda|A380]

Hello Magda|A380,

Welcome to Physics Forums!

For what it's worth, I calculated the same answer that you did (λ = 1.84 x 10^-14 m, to three significant figures).

Thanks collinsmark :)
Yeah, my books is known to be wrong sometimes and 1.84 x 10^-14 m still lies within the gamma ray wavelength range; so I'll accept it as the correct answer.