CBSE 2024 · Region 2 · Set 2 · Q26 · 3 marks
(a)Briefly explain de Broglie hypothesis for wave nature of matter.(b)Find the ratio of de Broglie wavelength associated with a proton and an alpha particle when both are(i)accelerated from rest through the same potential difference, and(ii)moving with the same kinetic energy.
(a)
Briefly explain de Broglie hypothesis for wave nature of matter.
(b)
Find the ratio of de Broglie wavelength associated with a proton and an alpha particle when both are
(i)
accelerated from rest through the same potential difference, and
(ii)
moving with the same kinetic energy.
Marking-scheme solution
(a)
Moving particles of matter display wave-like properties under suitable conditions.
The wavelength $\displaystyle \lambda$ associated with a particle of momentum p is given as:
$\displaystyle \lambda=\frac{h}{p}=\frac{h}{m v}$
$\displaystyle \lambda$ is the attribute of a wave while momentum is a typical attribute of a particle.
(i)
$\displaystyle \lambda=\frac{h}{\sqrt{2 m e V}}$
$\displaystyle \frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{2 \times 4 m_{p} \times 2 e \times V}{2 \times m_{p} \times e \times V}}$
$\displaystyle =2 \sqrt{2}$
(ii)
$\displaystyle \lambda=\frac{h}{\sqrt{2 m K}}$
$\displaystyle \frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{2 \times 4 m_{p} \times K}{2 \times m_{p} \times K}}$
$\displaystyle =2$
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CBSE Class 12 Physics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.