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Chemistry Question on Developments Leading to the Bohr’s Model of Atom

  1. The energy associated with the first orbit in the hydrogen atom is –2.18×10–18 J atom–1. What is the energy associated with the fifth orbit ?
  2. Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
Answer

(i) Energy associated with the fifth orbit of hydrogen atom is calculated as:
E5=−(2.18×10−18)(5)2E_5 = \frac {-(2.18 × 10^{-18})}{(5)^2}
E5=−(2.18×10−18)25E_5 = \frac {-(2.18 × 10^{-18})}{25}
E5=−8.72×10−20JE_5= -8.72 × 10^{-20} J

(ii) Radius of Bohr's n thorbit for hydrogen atom is given by,
rn=(0.0529 nm)n2r_n= (0.0529 \ nm) n^2
For, n=5n = 5
r5=(0.0529 nm)(5)2r_5= (0.0529\ nm)(5)^2
r5=0.0529×25 nmr_5= 0.0529 \times 25\ nm
r5=1.3225 nmr_5= 1.3225 \ nm