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 $\left(\right.2n+1\left.\right)r_{1}$ , where $n$ is higher orbit
• C. increases by $\left(\right.2n+1\left.\right)r_{1}$ , 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 $x_{2}=r_{1}\left(n+1 \right)^{2}=r_{1}\left(n^{2} + 2 n + 1\right)$
$x_{2}-x_{1}=r_{1}\left(2n+1\right)$
If $n$ is higher orbit, then consecutive lower orbit $=n-1$
and $x_{2}^{'}=r_{1}\left( n-1 \right)^{2}=r_{1}\left(n^{2} - 2 n + 1\right)$
$x_{1}-x_{2}^{'}=r_{1}\times n^{2}-r_{1}\left(n^{2} - 2 n + 1\right)=r_{1}\times \left(2n-1\right)$