Please answer **Theory of Mirror Dark Matter**In the theory of mirror dark matter, all known particles have corresponding particles in the dark matter sector with the same charge but different mass. For example, there is a dark proton and a dark electron. Let’s assume the dark proton has a mass of 10 TeV/c² and the dark electron has a mass of 200 MeV/c², and that they combine to form a dark Hydrogen atom.**Problem Set**(a) Calculate the radius \( r_1 \) of the first Bohr orbit of dark Hydrogen.(b) Calculate the energy \( E_0 \) of the ground state of dark Hydrogen and the energy \( E_1 \) of the first excited state.(c) What is the wavelength of light emitted in the transition from the first excited state of dark Hydrogen to the ground state? What part of the electromagnetic spectrum does this wavelength belong to (e.g., UV, X-ray, Gamma, etc.)?

In the theory of mirror dark matter, all known particles have corresponding particles in the dark matter sector with the same charge but different mass, i.e. there is a dark proton, a dark electron, etc. Let's assume the dark proton has mass 10 TeV/c² and the dark electron has mass 200 MeV/c² and that they combine to form a dark Hydrogen atom. (a) Calculate the radius r₁ of the first Bohr orbit of dark Hydrogen. (b) Calculate the energy Eo of the ground state of dark Hydrogen and the energy E₁ of the first excited state. (c) What is the wavelength of light emitted in the transition from the first excited state of dark Hydrogen to the ground state? What part of the electromagnetic spectrum is this (UV, X-ray, Gamma, etc.)? there is a particle in

In the theory of mirror dark matter, all known particles have corresponding particles in the dark matter sector with the same charge but different mass, i.e. there is a dark proton, a dark electron, etc. Let's assume the dark proton has mass 10 TeV/c² and the dark electron has mass 200 MeV/c² and that they combine to form a dark Hydrogen atom. (a) Calculate the radius r₁ of the first Bohr orbit of dark Hydrogen. (b) Calculate the energy Eo of the ground state of dark Hydrogen and the energy E₁ of the first excited state. (c) What is the wavelength of light emitted in the transition from the first excited state of dark Hydrogen to the ground state? What part of the electromagnetic spectrum is this (UV, X-ray, Gamma, etc.)? there is a particle in