Question

a particle of mass 'm' is moving with velocity 'v'. if the mass of particle is halved and velocity is doubled then how will its de broglie wavelength will be affected?
a-wavelength will reduced to quarter of initial
b-wavelength will increase to double of initial
c-remains same
d-wavelength will reduced to half of initial
please explain it too​

Answer 1

Answer:

The De Broglie wavelength of the particle, when the mass is halved and velocity is doubled, remains the same.

Explanation:

De Broglie wavelength is used to determine the wave properties of matter. De Broglie wavelength, $\lambda =\frac{h}{mv}$ ,                                                                           where, h is the plank's constant, m and v are the mass and velocity of the particle.

That is, De Broglie wavelength is directly proportional to (1/mv). So, when the mass is halved and velocity is doubled, the net value of mv remains the same.

              $\begin{array}{l}\lambda =\frac{h}{\frac{m}{2}2v}\\\ \ =\ \frac{h}{mv}\end{array}$

Hence, the De Broglie wavelength, λ remains the same.