Shortest wavelength will correspond to maximum energy. As value of atomic number (Z) increases, the magnitude of energy in different energy states gets increased. Value of Z is maximum for doubly ionised lithium atom (Z = 3) among the given elements. Hence, wavelength corresponding to this will be least.
KEY CONCEPTS Emission Spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an atom or molecule making a transition from a high energy state to a lower energy state.
Bohrs Model
Bohr Model:
Niels Bohr applied classical mechanics, electromagnetism and Planck's quantum theory to modify the Rutherford's model and proposed his atomic model in 19t3. His model gives satisfactory explanation of stable atomic structure and emission of line spectra by hydrogen atom. He presented His theory in the form of 3 postulates.
Bohr's Postulates
Bohr Model:
Niels Bohr applied Classical mechanics, electromagnetism and Planck's quantum theory to modify the Rutherford's model and proposed his atomic model in 1913. His model gives satisfactory explanation of stable atomic structure and emission of line spectra by hydrogen atom. He presented his theory In the form of 3 postulates:
Postulate 1 : The electron In a hydrogen atom revolves in circular orbit around the nucleus with nucleus at the centre of ort>ll
The necessary centripetal force for circular motion is provided by electrostatic force of attraction between the positively charged nucleus and negatively charged electron.
Hydrogen atom consists of only one electron and the nucleus. Let an electron of mass m revolves with speed v in an orbit of radius r. the charge on nucleus must be +e to make atom electrically neutral.
The force of attraction between electron and nucleus is given by Coulomb's law:
F =
The centripetal force is given by
∴ Centripetal force = Electrostatic force of attraction.
=
Postulate 2:
The electron revolves around the nucleus only in those orbits tor which the angular momentum Is equal to an integral multiple of
, where h Is Planck's constant. These orbits are called stable or stationary (or permitted or quantized or Bohr orbits) and electron does not radiate energy whole revolving in these orbits i.e. Its energy remains constant and hence stability of atomic structure.
Angular momentum = lu
Where I is moment of inertia of electron about Its axis of revolution and ω is angular velocity given by ω =
Angular momentum = Iω =
mr2() = mvr
By 2nd postulate , angular momentum =
n ∴ mvr =
n Where n = 1 , 2 , 3 , 4 , ...
That is electrons revolve in only those orbits that satisfies the equation. The Integer -n' is called principal quantum number. It also designates the orbit number.
What is minimum angular momentum of electron in hydrogen atom?
Postulate 3:
When electron jumps from orbit of higher energy Jo an orbit of lower energy, It radiates energy in the form of quanta or photons.
The energy of emitted photon is equal to 1he difference between energies of two orbits in which transition is taking place.
Suppose an electron from nth higher orbit, jumps to pth lower orbit. Each
En and
Ep be the energies of electron in nth and pth orbit respectively, then
Energy radiated =
En−Ep According to Planck's quantum theory, energy is radiated in the form of packets or quanta.
with each quanta having energy equal to hu; where 'h' is Planck's constant and v is 1he frequency of emitted radiation
Energy radiated = hv
An electron does not radiate energy while revolving in stable orbit but it does so only when It jumps from higher orbit to lower orbit