First slide

Matter waves (DC Broglie waves)

Question

What will be the ratio of the de-Broglie wavelength of proton and o particle of same energy

Easy

A

2 :1
B

1 :2
C

4:1
D

1:4

Solution

$λ = \frac{h}{mv} = \frac{h}{\sqrt{2 mE}} E = \frac{1}{2} {mv}^{2} or 2 mE = m^{2} v^{2} or mv = \sqrt{2 mE} so \frac{λ_{p}}{λ_{α}} = \sqrt{(\frac{m_{α}}{m_{p}})} = \sqrt{\frac{4}{1}} = 2 or λ_{p} : λ_{α} = 2 : 1$

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