Question

A spectral line is obtained from a gas discharge tube at $5000A^o$ . If the rms velocity of gas molecules is ${10}^{5}m{s}^{-1}$ then the width of spectral line will be

• A. $3.3A^o$
• B. $4.8A^o$
• C. $7.2A^o$
• D. $9.1A^o$

Answer 1

The correct option is A $3.3A^o$

$\frac{\Delta \lambda }{\lambda }=\frac{v}{c}$

we have to find 2x$\Delta \lambda$ (width of spectral line)

and we have been given that v =${10}^5$m$s^{-1}$, $\lambda =5000A^o$ and 'c' is speed of light so that gives us

$\Delta \lambda =5/3$

and so width would be 10/3 = 3.3$A^o$