Question

Two lines, A and B, in the plot given below show the variation of de-Broglie wavelength, `lambda` versus `1//sqrt(V)`, where V is the accelerating potential difference, for two particles carrying the same charge. Which one of two represents a particle of smaller mass?

Answer 1

`:. lambda=(h)/(sqrt(2meV))rArr lambda=(h)/(sqrt(m).sqrt(2e)).(1)/(sqrt(V))`
`rArr (1)/(sqrt(m))=(sqrt(2e))/(h).((lambda)/(1//sqrt(V))) :. (1)/(sqrt(m))=(sqrt(2e))/(h)xx("Slope of "lambda & sqrt(V)"graph")`
`:. "Slope of B" gt "Slope of A"(1)/(sqrt(m_(B))) gt (1)/(sqrt(m_(A)))rArr sqrt(m_(B)) lt sqrt(m_(A)):. m_(B) lt m_(A)`
Therefore, line B represents a particle of smaller mass.