Velocity of electron in first orbit of hydrogen atom

Asked by admin @ 20/08/2021 in Chemistry viewed by 324 People

Q7) Calculate the velocity of electron in the first Bohr orbit of hydrogen atom. [Given:- Bohr radius = 0.529 Å, h = 6.626×10-34 Js, mass of the electron = 9.1×10-31 kg]

Answered by admin @ 20/08/2021

Answer : The velocity of electron in the first Bohr orbit of hydrogen atom is, $2.189\times 10^6m/s$

Explanation :

Formula used for velocity of electrons in Bohr orbit of hydrogen atom is :

$v=\frac{nh}{3\pi mr}$

where,

v = velocity of electron = ?

n = principle quantum number = 1

h = Planck's constant = $6.626\times 10^{-34}Js$

m = mass of electron = $9.1\times 10^{-31}Kg$

r = Bohr radius = $0.529A^o=0.529\times 10^{-10}m$

Conversion used : $1A^o=10^{-10}m$

Now put all the given values in the above formula, we get :

$v=\frac{1\times 6.626\times 10^{-34}Js}{3\times 3.14\times 9.1\times 10^{-31}Kg\times 0.529\times 10^{-10}m}$

$v=2.189\times 10^6m/s$

Therefore, the velocity of electron in the first Bohr orbit of hydrogen atom is, $2.189\times 10^6m/s$

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