Question

For $H-$ atom, as the orbit number increases, the distance between two successive orbits $(r_1=$ radius of first orbit $)$

• A. Increases by $2r_1$
• B. increases by $(2n+1)r_1$ , where $n$ is higher orbit
• C. increases by $(2n+1)r_1$ , where $n$ is lower orbit
• D. remains constant

Answer 1

Answer: (C)

Radius $\left(x_1\right)$ of $n^{\text{th }}$ orbit for $H$ -atom $=r_1\times n^2$
If $n$ is lower orbit, the next orbit $=n+1$
and $x_2=r_1{\left(n+1\right)}^2=r_1\left(n^2+2n+1\right)$
$x_2-x_1=r_1\left(2n+1\right)$
If $n$ is higher orbit, then consecutive lower orbit $=n-1$
and $x_2^{{}^{\prime }}=r_1{\left(n-1\right)}^2=r_1\left(n^2-2n+1\right)$
$x_1-x_2^{{}^{\prime }}=r_1\times n^2-r_1\left(n^2-2n+1\right)=r_1\times \left(2n-1\right)$