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Calculate the radius of the smallest Bohr orbit for a μ− bound to a nucleus of platinum (Pt195 with 78 protons and 117 neutrons). Compare with the approximate radius of the nucleus of platinum (remember that the radius of a proton or neutron is about 1 × 10−15 m, and the nucleons are packed closely together in the nucleus)

Calculate the radius of the smallest Bohr orbit for a μ− bound to a nucleus of platinum (Pt195 with 78 protons and 117 neutrons). Compare with the approximate radius of the nucleus of platinum (remember that the radius of a proton or neutron is about 1 × 10−15 m, and the nucleons are packed closely together in the nucleus)

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I am stuck on part c. Please only answer part c. Thank you!

(c) Calculate the radius of the smallest Bohr orbit for a μ− bound to a nucleus of platinum (Pt195 with 78 protons and 117 neutrons). Compare with the approximate radius of the nucleus of platinum (remember that the radius of a proton or neutron is about 1 × 10−15 m, and the nucleons are packed closely together in the nucleus).

(a) Predict the energy in eV of a photon emitted in a transition from the first excited state to the ground state in ev for a system consisting of a nucleus containing Z = 50 protons and just one electron. You need not recapitulate the entire derivation for the Bohr model, but think carefully about the changes you have to make to take into account the factor Z. eV (b) The negative muon (u-) behaves like a heavy electron, with the same charge as the electron but with a mass 207 times as large as the electron mass. As a moving u¯ comes to rest in matter, it tends to knock electrons out of atoms and settle down onto a nucleus to form a "one-muon" atom. For a system consisting of a nucleus of platinum (Pt195 with 78 protons and 117 neutrons) and just one negative muon, predict the energy in ev of a photon emitted in a transition from the first excited state to the ground state. The high-energy photons emitted by transitions between energy levels in such "muonic atoms" are easily observed in experiments with muons. ev (c) Calculate the radius of the smallest Bohr orbit for a µ bound to a nucleus of platinum (Pt195 with 78 protons and 117 neutrons). Compare with the approximate radius of the nucleus of platinum (remember that the radius of a proton or neutron is about 1 × 10-15 m, and the nucleons are packed closely together in the nucleus). smallest Bohr orbit r Bohr = approximate radius of nucleus r nucleus *
Transcribed Image Text:(a) Predict the energy in eV of a photon emitted in a transition from the first excited state to the ground state in ev for a system consisting of a nucleus containing Z = 50 protons and just one electron. You need not recapitulate the entire derivation for the Bohr model, but think carefully about the changes you have to make to take into account the factor Z. eV (b) The negative muon (u-) behaves like a heavy electron, with the same charge as the electron but with a mass 207 times as large as the electron mass. As a moving u¯ comes to rest in matter, it tends to knock electrons out of atoms and settle down onto a nucleus to form a "one-muon" atom. For a system consisting of a nucleus of platinum (Pt195 with 78 protons and 117 neutrons) and just one negative muon, predict the energy in ev of a photon emitted in a transition from the first excited state to the ground state. The high-energy photons emitted by transitions between energy levels in such "muonic atoms" are easily observed in experiments with muons. ev (c) Calculate the radius of the smallest Bohr orbit for a µ bound to a nucleus of platinum (Pt195 with 78 protons and 117 neutrons). Compare with the approximate radius of the nucleus of platinum (remember that the radius of a proton or neutron is about 1 × 10-15 m, and the nucleons are packed closely together in the nucleus). smallest Bohr orbit r Bohr = approximate radius of nucleus r nucleus *
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