If E and λ represent the energy and wavelength respectively of an electron, then the graph between log λ and log E will have

Question

If E and λ represent the energy and wavelength respectively of an electron, then the graph between log λ and log E will have (A) positive slope (B) negative slope (C) zero slope (D) infinite slope

Tardigrade Admin · Accepted Answer

λ=(h/√2 m E) ⇒ ln λ= ln ((h/√2 m))- ln √E ln λ= ln ((h/√2 m))-(1/2) ln E comparing with y=m x+C ln λ vs ln E will have a slope of -(1/2)

Q. If $E$ and $λ$ represent the energy and wavelength respectively of an electron, then the graph between log $λ$ and $lo g E$ will have

positive slope

negative slope

zero slope

infinite slope

$λ = \frac{h}{2 m E} \Rightarrow ln λ = ln (\frac{h}{2 m}) - ln E$
$ln λ = ln (\frac{h}{2 m}) - \frac{1}{2} ln E$ comparing with $y = m x + C$
$ln λ$ vs $ln E$ will have a slope of $- \frac{1}{2}$

Q. If E and λ represent the energy and wavelength respectively of an electron, then the graph between log λ and logE will have