Question

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the velocity of electron in excited state of h atom is
1.093 × 10 m\s
⛑ what is the circumference of the this orbit??
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Answer 1

Velocity = 2.18× 10^6 × 1 /n

velocity = 1.093× 10^ 6

1.093× 10^6 = 2.18× 10^6 × 1/n

1.093/2.18 = 1/n

1/2 = 1/n

n= 2

Radius = 0.53 n^2 × 10^-10

= 0.53 × 4 × 10^-10

= 2.12 × 10^-10 m

circumference = 2× 3.14× 2.12 × 10^-10

= 6.28× 2.12× 10^-10

= 13.31× 10^-10

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Answer 2

The velocity of an electron is given by the following formula :

V(electron) = (2.18 × 10^6 × z) / n

Where :

n = The number of the orbit

z = the atomic number of the element.

We do the substitution as follows :

1.093 × 10^6 = (2.18 × 10^6 × 1)/n

n = (2.18 × 10^6)/(1.093 × 10^6)

n = 1.9945

n = 2

Radius of the orbit = 0.53n^2

r = 0.53 × 4 = 2.12

Circumference = 2pie × r

= 2.12 × 2 × 3.142 = 13.32

The circumference of the orbit is thus given as 13.32.