Question

An alpha particle and a proton are accelerated separately by the potential difference of 2 V and ZV respectively but ratio of de Broglie wavelength of alpha particle to proton is 2. The value of 'Z/8' is ​

Answer 1

Answer:

The value of $\frac{Z}{8}$is 4.

Explanation:

As given, the potential of alpha and proton is 2v and Zv respectively the ratio of de Broglie wavelength of the alpha particle to proton is 2.

Let the mass of proton be m and charge on it is q. Therefore the mass of alpha particle will be 4m and the charge is 2q.

λρ = $\frac{h}{\sqrt{2mqZV} }$

λα = $\frac{h}{\sqrt{2mqV} }$

    = $\frac{h}{\sqrt{2(4m)(2q)2V} }$

as the ratio of de Broglie wavelength of the alpha particle to proton is 2, then

$\frac{\frac{h}{\sqrt{2mqZV} } }{\frac{h}{\sqrt{2(4m)(2q)2V} } } =\frac{1}{2}$

$\frac{8}{Z} = \frac{1}{4} \\Z=32$

The value of $\frac{Z}{8} = \frac{32}{8}$

                         = 4

Hence, the value of $\frac{Z}{8}$ is 4.