The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

Question

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is : (A) (h2/π2 m2 r3)  (B) (h2/8π2 m2 r3)  (C) (h2/ 4π2 m2 r3)  (D) (h2/4π m2 r3)

Tardigrade Admin · Accepted Answer

v=(l2/2 h ε0) r=(h2 ε0/π m e2) ⇒ ε0=(r π m e2/h2) (v2/r)=(l2 π m/4 h4 ε03)=(h2/4 r3 π2 m2)

Q. The acceleration of an electron in the first orbit of the hydrogen atom $(n = 1)$ is :

$\frac{h ^{2}}{π ^{2} m ^{2} r ^{3}}$

$\frac{h ^{2}}{8 π ^{2} m ^{2} r ^{3}}$

$\frac{h ^{2}}{4 π ^{2} m ^{2} r ^{3}}$

$\frac{h ^{2}}{4 π m ^{2} r ^{3}}$

$v = \frac{l ^{2}}{2 h ε _{0}}$
$r = \frac{h ^{2} ε _{0}}{πm e ^{2}}$
$\Rightarrow ε_{0} = \frac{r πm e ^{2}}{h ^{2}}$
$\frac{v ^{2}}{r} = \frac{l ^{2} πm}{4 h ^{4} ε _{0}^{3}} = \frac{h ^{2}}{4 r ^{3} π ^{2} m ^{2}}$

Q. The acceleration of an electron in the first orbit of the hydrogen atom (n=1) is :

π2m2r3h2​

8π2m2r3h2​

4π2m2r3h2​

4πm2r3h2​