Particle Collision: Calculate Photon Wavelength

[Air]

Homework Statement

The results of particle collisions are observed using particle detectors. Sometimes the products of these collisions are themselves unstable and decay to give further particles; the products of decay can be photons.

In one collision, a stationary $\pi^\circ$ meson is produced which then decays to give two gamma ray photons. The rest mass of the meson is $135 \ MeV/c^2$.

$\pi ^\circ \rightarrow \beta + \beta$​

Calculate the wavelength of each photon.

Homework Equations

$E = hf = \frac{hc}{\lambda}$

The Attempt at a Solution

How can I find $E$? I can carry on from that point but I don't know which equation to use to find $E$?

 

[gendou2]

The energy of the stationary meson is calculated using E = mc²

E_pi = m_pi*c² = 135 MeV / c² * c² = 135 MeV

 

[Moetasim]

To find the energy (E) of each photon, we can use the equation E = mc^2, where m is the rest mass of the particle and c is the speed of light. Since the rest mass of the \pi^\circ meson is 135 \ MeV/c^2, we can calculate the energy as follows:

E = (135 \ MeV/c^2) * (3*10^8 m/s)^2 = 1.215 * 10^-11 J

We can then use this value for E in the equation E = hf, where h is Planck's constant (6.626 * 10^-34 J*s) and f is the frequency of the photon. We can rearrange this equation to solve for the wavelength (λ) as follows:

λ = \frac{hc}{E}

Plugging in the values for h, c, and E, we get:

λ = \frac{(6.626 * 10^-34 J*s)(3*10^8 m/s)}{1.215 * 10^-11 J} = 5.151 * 10^-7 m

Therefore, the wavelength of each photon is approximately 5.151 * 10^-7 m or 515.1 nm.