If α =(h/4 π 2 m e2), then the correct expression to calculate of the circumference of the first orbit of hydrogen atom is

Question

If α =(h/4 π 2 m e2), then the correct expression to calculate of the circumference of the first orbit of hydrogen atom is (A) √4π hα (B) √2π hα (C) √4 h2π α (D) Both A and C

Tardigrade Admin · Accepted Answer

circumference =2π r 2× π × (n2 h2/4 π 2 m Z e2) n=1 Z=1 and (h/4 π 2 me2)=α Thus, 2× π × r =√4π hÎ± or √4 h2π Î±

Q. If $α = \frac{h}{4 π ^{2} m e ^{2}},$ then the correct expression to calculate of the circumference of the first orbit of hydrogen atom is

$4 πh α$

$2 πh α$

$4 h^{2} π α$

Both A and C

circumference $= 2 π r$

$2 \times π \times \frac{n ^{2} h ^{2}}{4 π ^{2} m Z e ^{2}}$

$n = 1$

$Z = 1$

and $\frac{h}{4 π ^{2} m e ^{2}} = α$

Thus, $2 \times π \times r$

$= 4 πh α$

or $4 h^{2} π α$

Q. If α=4π2me2h​, then the correct expression to calculate of the circumference of the first orbit of hydrogen atom is

4​πhα

2​πhα

4h2​πα