Using Bohr's model,the speed of an electron in the first orbit is A)3.14 $\times$ 10⁵ m/s B)1.09 $\times$ 10⁶ m/s C)1.37 $\times$ 10⁷ m/s D)2.19 $\times$ 10⁶ m/s E)None of these is correct.

Question

Quizplus · Accepted Answer

According to Bohr's model, the speed of an electron in the first orbit (n=1) can be calculated using the formula v = (Z * e^2)/(n * h), where Z is the atomic number, e is the electronic charge, h is the Planck's constant and n is the principal quantum number.

For hydrogen atom (Z=1), substituting the values in the formula we get, v = (1 * (1.6022 x 10^-19)^2) / (1 * (6.6261 x 10^-34)) = 2.19 x 10^6 m/s.

Converting to scientific notation and rounding off, we get the answer as 2.19 x 10^6 m/s or 2.19 x 10^16 Å/s or 2.19 x 10^8 pm/s  or 2.19 x 10^10 cm/s or 2.19 x 10^4 km/s. Among the given options, only option D matches this value. Therefore, the correct answer is D.

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