If the kinetic energy of a particle is increa | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The de Broglie wavelength $\lambda$ is given by the formula $\lambda = \frac{h}{\sqrt{2mK}}$, where $h$ is Planck's constant, $m$ is the mass of t

Vedclass · Accepted Answer

$75$

Vedclass · Answer

(B) The de Broglie wavelength $\lambda$ is given by the formula $\lambda = \frac{h}{\sqrt{2mK}}$, where $h$ is Planck's constant, $m$ is the mass of the particle, and $K$ is the kinetic energy.From this relation, we see that $\lambda \propto \frac{1}{\sqrt{K}}$.Let the initial kinetic energy be $K_1 = K$ and the final kinetic energy be $K_2 = 16K$.The ratio of the wavelengths is $\frac{\lambda_2}{\lambda_1} = \sqrt{\frac{K_1}{K_2}} = \sqrt{\frac{K}{16K}} = \sqrt{\frac{1}{16}} = \frac{1}{4} = 0.25$.Thus, $\lambda_2 = 0.25\lambda_1$.The percentage change in wavelength is given by $\frac{\lambda_1 - \lambda_2}{\lambda_1} 	imes 100\%$.Substituting the values, we get $\frac{\lambda_1 - 0.25\lambda_1}{\lambda_1} 	imes 100\% = 0.75 	imes 100\% = 75\%$.

If the kinetic energy of a particle is increased by $16$ times, the percentage change in the de Broglie wavelength of the particle is......... $\%$

Similar Questions

$A$ proton and an $\alpha$-particle are accelerated through a potential difference of $100\, V$. The ratio of the wavelength associated with the proton to that associated with an $\alpha$-particle is

If the kinetic energy of a free electron is doubled,by what factor does its de Broglie wavelength change?

If the de Broglie wavelength of a dust particle of mass $1.0 \times 10^{-9} \,kg$ is $3 \times 10^{-25} \,m$, then the speed of the particle is . . . . . . . $\left(h=6.625 \times 10^{-34} \,J \,s\right)$

The energy that should be added to an electron to reduce its de-Broglie wavelength from $\lambda$ to $\frac{\lambda}{2}$ is $n$ times the initial energy. The value of $n$ is

The de-Broglie hypothesis treated electrons as

Vedclass Test Series

Exam Paper Generator

Online Exam Module