A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ . An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ . The ratio of kineti

Question

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ . An alpha particle having certain kinetic energy has the same de-Brogle wavelength λ . The ratio of kinetic energy of proton and that of alpha particle is :

TestHub · Accepted Answer

As we know, de Broglie wavelength is given by,

$λ = \frac{h}{p}$

Now kinetic energy can be written as,

$K = \frac{1}{2} m v^{2} = \frac{p^{2}}{2 m} = \frac{h^{2}}{2 m λ^{2}}$

Therefore,

$K \propto \frac{1}{m}$

Hence, required ratio

$\frac{K_{p}}{K_{α}} = \frac{m_{α}}{m_{p}} = 4 \Rightarrow m_{α} : m_{p} = 4 : 1$

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