Chemistry · Bohr model of a hydrogen atom: its postulates, derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr's model
In an atom two electrons move around the nucleus in circular orbits of radii and
In an atom two electrons move around the nucleus in circular orbits of radii and \( 4 \mathrm{R} \). The ratio of the time taken by them to complete one revolution is:
- A. 1: 4
- B. 4: 1
- C. 1: 8
- D. 8: 7
Step-by-step solution
According to Bohr's model, the time period T of an electron in a circular orbit is proportional to r^(3/2) (since T ∝ r^(3/2) from T = 2πr/v and v ∝ 1/√r). Given radii R and 4R, the ratio T1:T2 = (R)^(3/2) : (4R)^(3/2) = 1 : 4^(3/2) = 1 : 8.
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