If the kinetic energy of a particle is reduced to half, de-Broglie wavelength becomes

Question

If the kinetic energy of a particle is reduced to half, de-Broglie wavelength becomes (A)  2 times (B)  (1/√2) times (C)  4 times (D)  √2 times

Tardigrade Admin · Accepted Answer

The de-Broglie wavelength is inversely proportional to the square root of kinetic energy.
Hence,

\frac{λ _{1}}{λ _{2}} = \frac{( K E ) _{2}}{( K E ) _{1}}

Given that,

(K E)_{2} = \frac{1}{2} (K E)_{1}

Then,

\frac{λ _{1}}{λ _{2}}

or,

λ_{2} = 2 λ_{1}

Thus, de-Broglie wavelength becomes

2

times to the original wavelength.

Q. If the kinetic energy of a particle is reduced to half, de-Broglie wavelength becomes