Question

The most general form of momentum used in quantum mechanics is

• A. $p=mv$
• B. $p=\frac{E}{C}$
• C. $p=\frac{h}{\lambda }$
• D. $p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$

Answer 1

The correct option is C $p=\frac{h}{\lambda }$

In quantum mechanics energy of the particle is
$E=h\nu$
where, h is plank's constant, $\nu$ is frequency.
But according to mass-energy relation
$E=m{c}^2$
where, $m$ is mass of the particle and c is velocity of light.
$mc=\frac{E}{c}=\frac{h\nu }{c}$
$p=\frac{h}{\lambda }$
$\lambda$ is the wavelength of particle.