How many revolutions does an electron complete in one second in the first orbit of hydrogen atom?

Engineering

Physics

Bohrs Model of Atom

Calculus

Photoelectric Effect Einsteins Equation

Question

How many revolutions does an electron complete in one second in the first orbit of hydrogen atom?

A

6.62 × 10⁵

B

6.62 × 10¹⁵

C

6.62 × 10¹⁰

D

1.62 × 10¹⁵

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The radius of first orbit, r₁ = 0.53 × 10^–10m

Thus, circumference of this orbit, p = 2πr₁ = 2π × (0.53 × 10^–10) = 3.33 × 10^–10m

The speed of first orbit is approximately, v₁ = c/137 =

\frac{3 \times 10^{8}}{137}

= 2.19 × 10⁶m/s

Time period, T = p/v₁ =

\frac{3.33 \times 10^{- 10}}{2.19 \times 10^{6}}

= 1.52 × 10^–16s

The number of revolutions per sec is the frequency.

So, the frequency of the revolutions,

f = \frac{1}{T} = \frac{1}{1.52 \times 10^{- 16}}

= 6.6 × 10¹⁵