The de Broglie wavelengths of a proton and an | vedclass

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(D) The de Broglie wavelength is given by $\lambda = \frac{h}{p} = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is mass,and $v$ is velocity.From t

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$8: 1$

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(D) The de Broglie wavelength is given by $\lambda = \frac{h}{p} = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is mass,and $v$ is velocity.From this,the velocity is $v = \frac{h}{m\lambda}$.For a proton,$m_p = m$ and $\lambda_p = \lambda$. For an $\alpha$ particle,$m_\alpha = 4m$ and $\lambda_\alpha = 2\lambda$.The ratio of velocities is $\frac{v_p}{v_\alpha} = \frac{h / (m_p \lambda_p)}{h / (m_\alpha \lambda_\alpha)} = \frac{m_\alpha}{m_p} 	imes \frac{\lambda_\alpha}{\lambda_p}$.Substituting the values: $\frac{v_p}{v_\alpha} = \frac{4m}{m} 	imes \frac{2\lambda}{\lambda} = 4 	imes 2 = 8$.Therefore,the ratio is $8: 1$.

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be:

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