A radioactive sample has a certain number N of unstable nuclei that are emitting 4.5 MeV...

A radioactive sample has a certain number N of unstable nuclei that are emitting 4.5 MeV gamma rays with a half-life of 1.5 hours. If the rate of radioactive heating of the sample due to these decays is 13 watts, how many unstable nuclei are initially in the sample?

AND

A muon at rest decays into an electron, an anti-electron neutrino, and a muon neutrino. After the decay, the electron has a total energy of 52.85 MeV and the anti-electron neutrino has an energy of 20 MeV. What is the energy of the muon neutrino (in MeV, closest answer)?

AND

*Suppose that a particle of mass m is confined to a region of width a. Its energy in the ground state must be of order (the particle is non-relativistic)–

(1) \bar{h} ^2/(ma^2 ). (2) 2 eV. (3) \bar{h} /a. (4) \bar{h} ^2 *am. (5) \bar{h} ^2/(ma).

*(don't truly comprehend this last one specially-thanks.)

Solutions

Expert Solution

Above is the solution for first question

I have used the basic formula of radioactivity and since time is not specified I have taken it to be at t=0 and since the exact equation is not known I have expressed the answer in equivalents of gamma particles and generally it is taken to be 1.

The answer to the second question is above. I have considered the rest masses of both neutrinos to be zero for calculation purpose and since the answer need not be accurate to thousandth of an eV.

I hope the answer is clear

genius_generous answered 1 week ago

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