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(c) Calculate the velocity of the electron in the ground state of hydrogen. Express your answer as a percentage of the speed of light in a vacuum. Show that the total energy of the electron is equal to the negative value of its kinetic energy. Calculate all energies in units of electron volts. [5] (d) The electron in a hydrogen atom is replaced by a muon, which has a mass approximately 200 times greater than that of the electron. Calculate the wavelength of the $n = 2$ to $n = 1$ transition in muonic hydrogen. In what part of the electromagnetic spectrum does this transition belong? [6] (e) An excited electron in a singly-ionised helium atom (He$^+$ ion) makes a transition from the $n = 6$ state to the $n = 2$ state. Calculate the energy of the emitted photon in the Bohr model. Determine whether or not this photon could be absorbed by a hydrogen atom in its ground state. [5]

          (c) Calculate the velocity of the electron in the ground state of hydrogen.
Express your answer as a percentage of the speed of light in a vacuum.
Show that the total energy of the electron is equal to the negative value of
its kinetic energy. Calculate all energies in units of electron volts.
[5]
(d) The electron in a hydrogen atom is replaced by a muon, which has a mass
approximately 200 times greater than that of the electron. Calculate the
wavelength of the $n = 2$ to $n = 1$ transition in muonic hydrogen. In what
part of the electromagnetic spectrum does this transition belong?
[6]
(e) An excited electron in a singly-ionised helium atom (He$^+$ ion) makes a
transition from the $n = 6$ state to the $n = 2$ state. Calculate the energy of
the emitted photon in the Bohr model. Determine whether or not this photon
could be absorbed by a hydrogen atom in its ground state.
[5]

(c) Calculate the velocity of the electron in the ground state of hydrogen.
Express your answer as a percentage of the speed of light in a vacuum.
Show that the total energy of the electron is equal to the negative value of
its kinetic energy. Calculate all energies in units of electron volts.
[5]
(d) The electron in a hydrogen atom is replaced by a muon, which has a mass
approximately 200 times greater than that of the electron. Calculate the
wavelength of the n = 2 to n = 1 transition in muonic hydrogen. In what
part of the electromagnetic spectrum does this transition belong?
[6]
(e) An excited electron in a singly-ionised helium atom (He^+ ion) makes a
transition from the n = 6 state to the n = 2 state. Calculate the energy of
the emitted photon in the Bohr model. Determine whether or not this photon
could be absorbed by a hydrogen atom in its ground state.
[5]

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