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).  

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.

SIMILAR QUESTIONS

Q1

Which energy state of the triply ionized beryllium (Be+++) has the same orbital radius as that of the ground state of hydrogen? Compare the energies of the two states. 

Q2

Calculate the speed of an electron revolving in the first orbit around the nucleus of a hydrogen atom in order that in order that it may not be pulled into the nucleus by electrostatic attraction.

Q3

Determine the speed of electron in the n = 3 orbit of He+. Is the non-relativistic approximation valid? Datas as above.  

Q4

The total energy (potential + kinetic) of an electron in the ground state of Bohr model of hydrogen atom is –13.6 eV. Obtain the values of the potential energy U and kinetic energy K in eV. Include –ve or +ve sign as required.

Q5

A muonic hydrogen atom is a bound state of a negatively-charged muon  of mass 207me and a proton and the muon orbits around the proton. Obtain the radius of its first Bohr orbit.

 

 

Q6

The energy of an electron in an excited hydrogen atom is –3.4 eV. Calculate the angular momentum of the electron according to Bohr’s theory. Planck’s constant .  

Q7

A hydrogen atom rises from its n = 1 state to the n = 4 state by absorbing energy. If the potential energy of the atom in n = 1 state be –13.6 eV, thencalculate : potential energy in n = 4 state. 

Q8

The ionization energy of the hydrogen atom is given to be 13.6 eV. A photon falls on a hydrogen atom which is initially in the ground state and excites it to the n = 4 state.  Calculate the wavelength of the photon. 

Q9

An electron of energy 20 eV collides with a hydrogen atom in the ground state. As a result, the atom is excited to a higher energy state and the electron is scattered with reduced velocity. The atom subsequently returns to its ground state with emission of radiation of wavelength . Find the velocity of the scattered electron.

 

     

Q10

The de Broglie wavelength of a neutron at 927ois . What will be its wavelength at 27oC?