Question

An electron travels with a velocity of $xm{s}^{-1}$. For a proton to have the same de-Broglie wavelength, the velocity will be approximately:

• A. $\frac{1840}{x}$
• B. $\frac{x}{1840}$
• C. $1840x$
• D. $x$

Answer 1

The correct option is B $\frac{x}{1840}$

We know that:
de-Broglie wavelength $\Rightarrow \lambda =\frac{h}{p}$
$1840\times M_e=M_p$
$\frac{h}{(MV{)}_e}=\frac{h}{(MV{)}_p}$
$\frac{h}{M_e\times x}=\frac{h}{1840\times M_e\times V_p}$
$V_p=\frac{x}{1840}$