Question

Every atom is composed of a nucleus made of protons and neutrons (hydrogen-1 has no neutrons). The nucleus is surrounded by a cloud of electrons. The electrons in an atom are bound to the atom by the electromagnetic force, and the protons and neutrons in the nucleus are bound to each other by the nuclear force.Read para and answer(i)An electron in H-atom jumps from third energy level to first energy level.The change in potential energies of electron is
(ii)The ratio of highest possible wawelength to lowest possible wawelength of balmer series is
(iii)The wave number of first line of Balmer series of h is x cm^-1.Tje wave number of first line of be^+3 is
Please tell all questions with detailed explanations.

Answer 1

Energy associated with an electron in an energy state n or principal quantum number n is given by

En  = - R_H / n²  , with n = 1 or more, 
       where R_H = Rydberg constant = 2.18 * 10^-18 Joules

Change in energy =  E1 - E3  = - 2.18 * 10^-18 [ 1 - 1/3² ]  Joules
                           = - 1.937 * 10^-18 J

2)
     wavelength is given by
         λ = 365.2 * n² / (n² - 2²) nanometers , where n = 3, 4 , 5, ..... infinity
       highest / lowest =           ( λ for n= 3) / (λ for n = infinity)
                       = 365.2 * 9 / 365.2 * 1  = 9

3) 
  wave number of v of balmer series can be given as
        v = 109.677 * Z² * (1/2² - 1/n²)  cm⁻¹ , where    n = 3, 4, ....... infinity
           Z = atomic number of the atom

     Be has an atomic number Z of 4.
           Z = 1  for hydrogen.
         so  wave number for beryllium is 16 x  cm⁻¹ . 
   The energy of the electron transitions will be 16 times.  SO wavelength is divided by 16 and frequency and wave number are multipliedby 16