The speed of electrons in a scanning electron | vedclass

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Question

(A) The resolving power $(RP)$ of a microscope is inversely proportional to the de Broglie wavelength $(\lambda)$ of the particles used,i.e.,$RP \prop

Vedclass · Accepted Answer

$1837$

Vedclass · Answer

(A) The resolving power $(RP)$ of a microscope is inversely proportional to the de Broglie wavelength $(\lambda)$ of the particles used,i.e.,$RP \propto \frac{1}{\lambda}$.The de Broglie wavelength is given by $\lambda = \frac{h}{p} = \frac{h}{mv}$,where $h$ is Planck's constant,$m$ is the mass,and $v$ is the velocity.Substituting this into the expression for resolving power,we get $RP \propto \frac{1}{h/mv} = \frac{mv}{h}$.Since $h$ and $v$ are constant for both cases,$RP \propto m$.Therefore,the ratio of the resolving power of the proton microscope $(RP_p)$ to the electron microscope $(RP_e)$ is $\frac{RP_p}{RP_e} = \frac{m_p}{m_e}$.Given that the mass of a proton $m_p \approx 1837 	imes m_e$,the resolving power changes by a factor of $1837$.

The speed of electrons in a scanning electron microscope is $1 \times 10^{7} \, m/s$. If protons having the same speed are used instead of electrons,then the resolving power of the scanning proton microscope will be changed by a factor of:

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