Correct Answer - Option 1 : 75
CONCEPT:
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Relationship between Momentum (p) and Kinetic Energy (k): The momentum is equal to the square root of twice of kinetic energy and mass.
P = √ (2K m)
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De Broglie wavelength (λ): The wavelength associated with any particle in motion is known as De Broglie wavelength. It is given as
λ = h / p
h is Planck's constant, p is momentum.
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Relationship between De Broglie wavelength and Kinectic Energy: If we combine the above two concepts we can have the relationship between wavelength and kinetic energy as
\(λ =\frac{h}{\sqrt{2Km}}\)
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Percentage Change (x): The ratio of change in quantity (Q) to the actual quantity is called percentage change.
\(x = \frac{\Delta Q}{Q} \times 100%\)%
EXPLANATION:
Initially the De Broglie wavelength was λ, Kinetic energy K
\(λ =\frac{h}{\sqrt{2Km}}\)-- (1)
Kinetic Energy increased 16 times, then new kinetic energy K' = 16K
then new De Broglie wavelength
\(λ' =\frac{h}{\sqrt{2K'm}} = \frac{h}{\sqrt{2(16K)m}} \)
⇒ \(λ' = \frac{1}{4}\frac{h}{\sqrt{2Km}} \)--- (2)
Putting (1) in (2) we get
λ' = λ / 4
Change in wavelength = λ - λ' = λ - λ / 4
∆λ = 3 λ / 4
Percentage change
\( \frac{3\lambda /4}{\lambda} \times 100% = 75 %\) = 75 %
So, the percentage change is 75 %
