Question

An electron make transition from orbit number $N$ to $P^{th}$ orbit in $H-$atom and emit the photon of wavelength $\left(\lambda \right)$. In orbit $P$, velocity of electron in $H-$atom is maximum. Which of the following wavelength $\left(\lambda \right)$ is not possible?

(Where $1/R=912A)$

• A. $1216\stackrel{o}{A}$
• B. $972.8\stackrel{o}{A}$
• C. $1026\stackrel{o}{A}$
• D. $3973\stackrel{o}{A}$

Answer 1

The correct option is A $1216\stackrel{o}{A}$

Velocity of an electron is given by,

$v$ $\alpha$ $\frac{1}{n}$ hence, velocity of an electron is maximum for $n=1$. Therefore, the value of $pth$ orbit is 1. Now $N$ can take values $2,3,4,...$

Wavelength of an electron is given by $\frac{1}{\lambda }=R(\frac{1}{p^2}-\frac{1}{N^2})$

For $N=2$ $\lambda =1216A^0$

$N=3$ $\lambda =1026A^0$

$N=4$ $\lambda =972A^0$

Hence highest value for $\lambda =1216A^0$ hence it cannot have value greater than that.

Therefore correct option is $A$.