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Structure Of Atom

Question
CBSEENCH11005297

How has Bohr’s theory helped in calculating the energy of hydrogen electror in the ground state and also in the excited state?

Solution
The energy of hydrogen electron is
space space straight E subscript straight H space equals space fraction numerator negative 2 straight pi squared m e to the power of 4 over denominator straight n squared straight h squared end fraction
where m = mass of electron
e = charge on electron
h = Planck's constant
n = integer with value, 1, 2, 3, 4,  etc.
By substituting the values, we have,
space space space straight E subscript straight H space end subscript space equals space fraction numerator negative 2.17 space cross times space 10 to the power of negative 18 end exponent over denominator straight n squared end fraction straight J space per space atom
space space space space space space equals space fraction numerator negative 1311.8 over denominator straight n squared end fraction kJ space mol to the power of negative 1 end exponent
By assigning different values to the energy of hydrogen electron in ground state and different excited states can be calculated.

From the above table, it is obvious that negative value of energy keeps on decreasing as the electron moves from ground state to the higher energy states.