Question

Obtain an expression for the ratio of the accelerating potentials required to accelerate a proton and an alpha particle to have same de-Broglie wave lengh associated with them.

Answer 1

Answer:

the ratio of the accelerating potentials required to accelerate a proton and an alpha particle to have same de-Broglie wave lengh associated with them is 8 : 1

Explanation:

As we know that de Broglie wavelength of accelerating potential charge is given as

$\lambda = \frac{h}{\sqrt{2mqV}}$

now if the de broglie wavelength of proton and alpha particle is same

then we have

$\frac{h}{\sqrt{2m_{\alpha}q_{\alpha}V_{\alpha}}} = \frac{h}{\sqrt{2m_{p}q_{p}V_{p}}}$

now we have

$m_{\alpha} = 4m_{p}$

$q_{\alpha} = 2q_{p}$

so we have

$4m_p2q_p V_{\alpha} = m_pq_pV_p$

so we have

$\frac{V_p}{V_{\alpha}} = 8$

#Learn

Topic : de Broglie Wavelength

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