Two points on a log–log plot of de Broglie wavelength versus speed for identical…

PHYSICS · Single correct · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter

Problem

Two points on a log–log plot of de Broglie wavelength

\lambda

versus speed

v

for identical particles are recorded as: Point P:

v = 2.0\times10^{5}\,\text{m\,s}^{-1}

\lambda = 3.0\times10^{-9}\,\text{m}

Point Q:

v = 5.0\times10^{5}\,\text{m\,s}^{-1}

\lambda = 1.2\times10^{-9}\,\text{m}

Assuming a power-law dependence

\lambda \propto v^{n}

, the value of

n

is approximately (a)

-0.5

(b)

-1

(c)

-0.8

(d)

-1.2