Question

if the kinetic energy of a particle is increased by 44% then the percentage decrease in its De-Broglio wavelength will
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(16.6
(2) 1.66
(3) 16.6
(a) 61.6
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Answer 1

Answer:

HI to be a little bit of a new one and I have to go to sleep now so I don't know what to do with the kids to the hospital for a few 61.6us

Answer 2

Answer:

The deBroglie wavelength decreases by 16.67%.

Explanation:

DeBroglie wavelength λ associated with a particle is given by

$\lambda=\dfrac{h}{p}$

where h is the Planck's constant and p is the momentum.

The relation between the kinetic energy and momentum of a particle of mass m is given by

$E= \dfrac{p^{2}}{2m}$

where E is the kinetic energy.

Rewriting the formula, we get ${p=\sqrt{{2m}E}$

Substituting in deBroglie's wavelength, $\lambda=\dfrac{h}{\sqrt{2mE} }$

Since m and h are constants, $\lambda \propto \dfrac{1}{\sqrt{E} }$

For initial kinetic energy $E_1$, let the deBroglie wavelength be

$\lambda_1 \propto \dfrac{1}{\sqrt{E_1} }$                                                                                    ....(1)

When the kinetic energy is increased by 44%, then the new kinetic energy is $E_1+44\%\times E_1=1.44E_1$.

Thus, the new deBroglie wavelength is  $\lambda_2 \propto \dfrac{1}{\sqrt{1.44E_1} }$           ....(2)

Taking the ratio of the equations (1) and (2),  

$\dfrac{\lambda_1}{\lambda_2} =\dfrac{\dfrac{1}{\sqrt{E_1} }}{\dfrac{1}{\sqrt{1.44E_1} }} =\dfrac{\sqrt{1.44E_1}}{\sqrt{E_1} }$

$\implies \dfrac{\lambda_1}{\lambda_2} =\sqrt{1.44}=1.2$

$\implies \lambda_2=\dfrac{\lambda_1}{1.2}$

Decrease in the deBroglie wavelength,

$\Delta\lambda = \lambda_1-\lambda_2=\lambda_1-\dfrac{\lambda_1}{1.2}$

$=\dfrac{1.2\lambda_1-\lambda_1}{1.2}=\dfrac{0.2\lambda_1}{1.2}=\dfrac{\lambda_1}{6}$  

Thus, the percentage decrease in the deBroglie wavelength is

$\dfrac{\Delta\lambda}{ \lambda_1}\times 100= \dfrac{\dfrac{\lambda_1}{6}}{ \lambda_1}\times 100$

$=\dfrac{\lambda_1}{6}\times \dfrac{1}{ \lambda_1}\times 100=16.67\%$

Therefore, the deBroglie wavelength decreases by 16.67%.

As the options are not clear, nearby correct answer is option 3.