Q. 9 3.7( 3 Votes )

Define ionization energy.

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

OR

Calculate the shortest wavelength of the spectral lines emitted in Balmer series. [Given Rydberg constant, R = 107 m-1]

Answer :

Ionization energy is defined as the minimum amount of energy required to remove an electron from the outermost orbit of a neutral atom in it’s ground state (in other words ionize the atom or put positive charge on it) , so in case of an hydrogen atom it is the energy required to pull out the electron from hydrogen atom


H + Energy -> H + + e-


H is the hydrogen atom, H + is the hydronium ion formed after removal of an electron from a Hydrogen atom


For a hydrogen atom ionization energy of an electron is given by the relation


E = me4/8𝜺0h2


Where E is the ionization Energy, e is a charge of an electron, 𝜺0 is the permittivity of free space, h is Planck’s constant


So we can see e, 𝜺0,h are constants so ionization is directly proportional to mthe ass of ethe lectron, now electron is replaces by a particle having sthe ame charge as of electron and 200 times the mass of an electron so ionization energy becomes


E’ = 200me4/8𝜺0h2 = 200E


i.e. Ionization energy is increased and becomes 200 times the original value, i.e. more energy is required to pull out an electron from neutral hydrogen atom in the ground state.


OR


We know in an hydrogen atom a negatively charged electron is revolving around nucleus of hydrogen consisting of one proton, orbit is the well-defined circular path in which electron revolves around the nucleus these orbits have different energy level and electron have different speed depending upon the orbit in which it is revolving, the movement of electron can be characterized by state such as n = 1 for orbiting in the first orbit, n = 2 for orbiting in the second orbit and so on, the energy of n = 1 state is lowest and other states increase with n , when an electron absorbs energy in the form of electromagnetic radiations it jumps from lower energy level to higher energy level or higher states and when electron in higher energy state jumps to lower energy state it emits energy in form of electromagnetic waves, when an electron in a higher energy state(n >2 ) jumps to n = 2 state the spectrum formed due to emission of electromagnetic waves is called Balmer series


As has been shown in the figure



the wavelength of electromagnetic radiation emitted is given by the relation



Where 𝜆 is the wavelength of electromagnetic radiation emitted, R is Rydberg Constant , R = 107m-1 , nf is fthe inal state of ean lectron and ni is the initial state of ethe lectron, for Balmer series , since ethe lectron is jumping to sthe econd orbit so


nf = 2


now for 𝜆 to be minimum , should be maximum, i.e. should be maximum , i.e. should be minimum


so if we assume electron to be coming from infinitely far away orbit or infinity


i.e.


so equation becomes



i.e 𝜆 = 4 × 10-7 m


so shortest wavelength of the spectral lines emitted in Balmer series is 4 × 10-7 m


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