A proton captures a free electron whose kinetic energy is zero and forms a hydrogen atom of lowest energy-level (n = 1). If a photon is emitted in this process, what will be the wavelength of radiation? In which region of electromagnetic spectrum, will this radiation fall? (Ionisation potential of hydrogen atom = 13.6 V, ). : Kaysons Education

Question

A proton captures a free electron whose kinetic energy is zero and forms a hydrogen atom of lowest energy-level (n = 1). If a photon is emitted in this process, what will be the wavelength of radiation? In which region of electromagnetic spectrum, will this radiation fall? (Ionisation potential of hydrogen atom = 13.6 V, ).

medium

Solution

Correct option is

910 Å

The ionization potential of hydrogen atom is 13.6 volt. This means that to ionise the hydrogen atom, 13.6 eV of energy is required. Normally an atom is ionised from its lowest energy level (n = 1).

Hence the lowest energy of the electron in the hydrogen atom is

The kinetic energy of the given electron is zero. Hence the loss of energy of electron in forming hydrogen atom of n = 1 state is

If the wavelength of the emitted photon be , then

Substituting,

, and the given values of hand c, we get

This radiation will fall in the far ultra-voilet region of the electromagnetic spectrum.

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