Atmospheric neutrinos are produced from the cascading decays of cosmic pions (π^​±) to stable particles. Ignoring all other neutrino sources, the ratio of muon neutrino (v_​μ+ v ̅_​μ ) flux to electron neutrino (v_e+ v ̅_e ) flux in atmosphere is expected to be closest to

Correct option is D

Solution:

​Cosmic rays primarily consist of protons, which primarily decay into pions upon impact with the atmosphere of the Earth. The pions decay according to

​$$\pi^+ \rightarrow \mu^+ + \nu_\mu$$ 

and

​$$\pi^- \rightarrow \mu^- + \bar{\nu}_\mu$$

Then the most subsequent decay is the following:

$$\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_\mu$$ 

and

​$$\mu^- \rightarrow e^- + \bar{\nu}_e + \nu_\mu$$

The total number of muon neutrino (ν_​μ + ν̅_​μ) particles produced is 1 + 1 + 1 + 1 = 4.

The total number of electron neutrino (ν_e + ν̅_e) particles produced is 0 + 0 + 1 + 1 = 2.

This implies that the ratio of muon neutrino (ν_​μ+ ν̅_​μ) flux to electron neutrino (ν_e + ν̅_e) flux in the atmosphere is 2:1.

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