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Energy Levels

How would the...

Question

How would the ionization energy change when electron in hydrogen atom is replaced by a particle of mass $200$ times that of electrons but having the same charge?

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Solution

The minimum energy, required to free the electron from the ground state of the hydrogen atom, is known as lonization Energy.
$E_{0} \propto m$
Therefore, lonization Energy will become 200 times.

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Q. Define ionization energy.
How would the ionization energy change, when an electron in hydrogen atom is replaced by a particle of mass 200 times that of the electron but having the same charge ?

Q. Imagine that the electron in a hydrogen atom is replaced by a muon (

μ

). The mass of muon particle is

207

times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be:

A formula analogous to the Rydberg formula applies to the series of spectral lines which arise from transitions from higher energy level to the lower energy level of hydrogen atom.
A muonic hydrogen atom is like a hydrogen atom in which the electron is replaced by a heavier particle, the 'muon'. The mass of the muon is about

207

times the mass of an electron, while the charge remains same as that of the electron. Rydberg formula for hydrogen atom is:

\frac{1}{λ} = R_{H} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] (R_{H} = 109678 {c m}^{- 1})

Ionization energy of muonic hydrogen atom is

Q. In Thomson experiment of finding

\frac{e}{m}

for electrons, beam of electrons is replaced by that of muons (particle with same charge as of electrons but mass 208 times that of electrons).
No deflection condition in this is case satisfied, if :

Q. In a Bohr atom the electron is replaced by a particle of mass 150 times the mass of the electron and the same charge. If

a_{0}

is the radius of the Bohr orbit, then that of the new atom will be

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