Question

(b)
If the kinetic energy of a particle is reduced to one-fourth
its initial value, how many times will the de Broglie wavelength
associated with it become ?​

Answer 1

Answer:

half of its kinetic energy

Answer 2

The new de Broglie wavelength is 2 times of initial wavelength.

Explanation:

Given that,

If the kinetic energy of a particle is reduced to one-fourth  its initial value,

We know that,

The de Broglie wavelength is

$\lambda\prooto\dfrac{1}{p}$

We know that,

$p=\sqrt{2mk}$

Where, k = kinetic energy

Put the value into the formula

$\lambda\propto\dfrac{1}{\sqrt{2mk}}$

$\lambda\propto\dfrac{1}{\sqrt{k}}$

We need to calculate the new de Broglie wavelength

Using formula of de Broglie wavelength

$\dfrac{\lambda_{1}}{\lambda_{2}}=\sqrt{\dfrac{k_{2}}{k_{1}}}$

Put the value into the formula

$\dfrac{\lambda_{1}}{\lambda_{2}}=\sqrt{\dfrac{1}{4}}$

$\lambda_{2}=2\lambda_{1}$

Hence, The new de Broglie wavelength is 2 times of initial wavelength.

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Topic :

https://brainly.in/question/9429853