(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
(i) Energy associated with the first orbit in the hydrogen atom is calculated as:
(ii) Radius of Bohr’s orbit for hydrogen atom is given by,
Q: 17. Calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen.
For the Balmer series, thus, the expression of wavenumber is given by,
Wave number is inversely proportional to wavelength of transition. Hence, for the longest wavelength transition, has to be the smallest.
For to be minimum, should be minimum. For the balmer series, a transition from is allowed. Hence, taking
Q: 18. What is the energy in joules, required to shift the electron of the hydrogen from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is
Energy (E) of the Bohr orbit of an atom is given by,
Z=atomic number of the atom
Ground state energy
Energy required to shift the electron from is given as:
Wavelength of emitted light
Q: 19. The electron energy in hydrogen atom is given by Calculate the energy required to remove an electron completely from the orbit. What is the longest wavelength of light in cm that can be used to cause this transition?
Energy required for ionization from is given by,
Here, is the longest wavelength causing the transition.